Nathan:
My advice" use the time your fingers are healing to read and study something of some interest or use to you. Machine shop work is mostly "head work"= being able to design or sketch the jobs to be done, doing the trigonometry to figure missing dimensions if angles, figuring tapers, figuring tap drill sizes and so much more, aside from figuring setups for the jobs on the machine tools and hot to do the jobs. Whether it is turning a simple shaft with a few different diameters, or something more complex, shop work requires some "head work". Time spent waiting for your fingers to heal can be time well spent. A human mind is an infinite and amazing thing, but it needs to be exercised and kept limber, and doing math in your head or designing stuff that requires some figuring is a good mental exercise.
As for your injured fingers, I can relate a couple of stories of how people got a little mileage out of there injuries. An uncle of mine had sustained an injury to the middle finger of his left hand when he was a kid. We never tired of asking: "Which finger got mauled when you were a kid ?" Needless to say, our uncle would not hesitate to stick up the middle finger of his left hand, and us kids would howl with laughter.
A high school machine shop teacher had served an apprenticeship before WWII in Berlin, Germany. He worked in a shop which produced worm gear reducers (gearboxes), and milling the "threads" on the worms was something this fellow did as an apprentice. As he told it, he had to set up a universal milling machine with a dividing head geared to the table feeds. Once the machine was taking a cut, he had to make sure the chips were cleared and cutting oil flooding the cutter and work. He went to clear the chips on day while his milling machine but, instead of using a brush, used his pinky finger. In nothing flat, the cutter had grabbed his pinky finger and taken off the top portion to the first joint. Doctors cleaned up the remaining finger and stitched a flap of skin over the stub end of the bone. This teacher, who was normally a very reserved and formal man, used to clown around with the stump of his pinky. One of his favorite gags was to stand in a crowded NY Subway car during rush hour and act like he was picking his nose with his pinky, having seemingly jammed it up a nostril a bit past the first joint. Naturally, some people around him would start shooting disgusted looks at him for picking his nose in public. He'd act like his pinky was stuck up in his nose, seemingly tugging his hand to pull the pinky free, grasping the wrist of the hand with the stuck pinky with his other hand. All of a sudden, he'd give a lurch and act like the pinky had come free from his nostril. Of course, he'd then look at the missing portion of the pinky, and start acting agitated, putting a thumb to cap the opposite nostril and attempting to "blow out the missing hunk of pinky". The effect had varying results- some people laughed, some rolled their eyes, some studiously ignored him, some kidded him, and some few stuffed shirts were so disgusted they moved out of his vicinity. This fellow was a fine shop teacher, and he was very safety conscious. We had an old machine shop for our classroom, with lineshafting and belts from the overhead to drive the machine tools. Despite the teacher's kidding around about the missing pinky, he was a stickler for safety and we had no accidents beyond an occasional small cut or bruise.
A couple of simple rules I follow religiously:
-I put on safety glasses with side shields as soon as I get into my shop or garage. I wear prescription glasses with ANSI listed safety lenses, but have found that these let small chips get over the top of the glasses and into my eyes. I do not need my prescription glasses for close work, so plain safety glasses work fine for me. I feel naked without them if I start working in my shop or garage. My wife has pulled a lot of chips and small pieces of welding slag out of my eyes over 35 years of marriage and hauled my butt to the ER when she could not get whatever it was out of my eyes. Standard practice in the ER is to numb your eye(s), dilate them, stain them with dye and then start looking for the foreign objects and scraping around to get them once found. You go home seeing "starbursts" of light since your pupil is now dilated and you get a prescription for an opthalmic antibiotic and maybe some eyedrops. Your eye feels like someone threw sand under the lid for a bit, and you are out of commission until the next day. Wear safety glasses and make sure they have side shields and shield across the top. Make sure they are clean and not too scratched up so you can clearly see your work.
-never leave a key in a lathe chuck or drill chuck an instant longer than you need to have it there to tighten, loosen, or center a job. The instant you are done using a chuck key, get it OUT of the chuck. Accidental starting of machine tools can send chuck keys flying with enough force to seriously injure anyone in their path. Oldtime machinists and shop teachers would holler murder at anyone who left a key in a chuck when it did not need to be there, and giving a young fellow a jab in the ribs or a swat "upside the head" while calling him a "Dummkopf" (dumb head in German) or far worse was standard practice.
-never grasp an end mill cutter or milling cutter barehanded, particularly to put it into an endmill holder or collet or to pull it out. I use a cloth shop rag.
-never touch, let alone grasp, the turning (chip) coming off a machine tool while cutting is in progress. If the turning is getting to be a problem, I use a wrench or similar to hook it or guide it. Never clean up chips while a machine tool is running. Never handle the chips barehanded, use a pair of leather gloves. If long chips are snarled in a bird's nest and won't come free of a machine tool, do not tug on them even with gloved hands. Sharp edged turning cut like razors and will slice thru a pair of leather gloves and into your fingers before you know it happened. Use pliers or wire cutters to deal with tangled chips.
-never stick your finger into a freshly bored or drilled hole- chances are there is a wicked burr or very sharp corner at the mouth of the hole and you can slice a finger and cut a tendon just that quick. Plenty of guys have done it.
-if your lathe has a quick change toolpost, remove the holder and toolbit when setting up a job in the lathe. One slip of your hand into a toolbit or parting tool and you will be bleeding. Similarly, remove the tailstock center when not immediately needed. One slip when you are setting up a job or reaching around the lathe and you can get nailed by the tailstock center on a smaller lathe.
-wrenches are a whole other matter, and slipping with a wrench has caused me to skin a handful of knuckles. Using the right sized wrench, trying not to use adjustable (aka "Crescent" wrenches), making sure the wrench is properly seated on the head of the bolt or on the nut and has room to turn with the fastener are all things to keep in mind. Adjustable wrenches, under heavy strain, can and do slip and chew the corners on nuts and bolts- and result in bruises and cuts for the user. A 12 point socket or 12 point box wrench may fit a nut or bolt properly, but if that fastener is made up too tight or has slightly rounded corners, under the strain you put on that wrench it will slip and send you flying. Use a 6 point socket on more ornery fasteners and have no chance of rounding the corners and slipping.
Lastly, make sure your tetanus shot is up to date, and keep a good first aid kit at hand.