Specially, since medicine is actually the most rare skill to increase from random events?
[only way to randomly raise medicine is from using Medkits, which already require base 40 medicine to even use, so if you have under 40 medicine, you can never randomly increase medicine anywhere. Just the limited static 'reading books' or 'college whatever'.]
This is why I prioritize first the academy classes, then the academics books, then the science books, and THEN the medical books. All of them (except for 1 of the science books) increase intelligence which boosts how much medical you get from those books. With high intelligence you can get a bit over 50 medicine from the books plus whatever you start with.
Does using doctor's kits actually have a chance to increase medical? I have never seen it do that so far but I only need them for tier 6 bounties so I've only used about 10-15 of them so far. I've actually considered switching to a doctor build specifically because it takes me so long to get to 40 medical normally which is annoying for my playstyle. Doctors start with more than that right from the get go so you could potentially grind it up around 60 or more with doctors kits before reading the books if you wanted to really maximize it.
I couldn't tell how much it increases your stim heals but the doctors kits are an absolute game changer for tier 6 bounties since it's nearly impossible to do those without losing someone unless you have some extra bonuses in place beyond a guaranteed hit by 4 plasma guns plus a guaranteed hit with Ayden's coil gun. That alone is not enough unless you get lucky and get one of the easier versions of it.
I still haven't managed to test whether Caitlyn can patch my main up with one if my main gets taken down. I'm hoping she can but she's currently a science professor and I haven't started working on her combat skills yet. Also haven't gotten the health implants for my main so for me to test it now I would probably have to take Caitlyn out with nothing but low tier mercs to make sure I was actually tanking.
Using low tiers plus Caitlyn for an extended period of time might be an interesting option for a doctor build. You could still do anything short of a tier 6 bounty probably and assuming Caitlyn can patch up the MC it wouldn't matter if someone gets taken down occasionally. It would take awhile to train up her combat skills but she starts off as a great quartermaster right from the get go with only a small amount of science training needed for her to be able to auto repair your duraplate (albeit slowly). Might have to get both Duraplate and Weave if you wanted to maximize her armor repair ability and switch between the two a bit to spread the damage around. She doesn't do it for free but she does do it a lot cheaper than the armor vendor.