I think most players aren't experiencing this, so if it's becoming a problem for you to enjoy the game, perhaps consider what you might do to change your play style a little to avoid the problem. But since I really don't know your play style or what might be the reason you're experiencing this, I can't really suggest any specific ways to improve things. Although it doesn't necessarily benefit playing stealth (assassin armor suggests that is what you're doing), maybe consider wearing the preacher armor set instead. It gives a big reduction to debuffs (crits). That might make the game more fun for you even if it doesn't necessarily benefit your particular build the way assassin armor does.
Maybe you're just getting hit a lot more than you think? My understanding is that the more times you get hit in a row, the more chance of a debuff (I might be wrong about that, though). I do tend to get infected a fair amount, but nothing serious. And that's mostly because I go straight into the fight almost every time without trying to be sneaky about it and so I get hit a LOT. But I can handle it, so I don't mind. And with the number of times I'm hit by attacks, my chance of debuffs right now (yes, right now I'm in tier 6 medium armor), is most likely under 5%.
As far as meds go, honey is the only thing that is ever a problem, and only in the early game. I find enough of everything else very quickly just in loot. And medical magazines are found in almost every medical loot pile it seems, so you should be able to max that fairly quickly if you're looting medical stuff. You can find these medical piles all over the place and basically any pop n pills crate also has medical magazines and they can be found elsewhere as well. It tends to be one of the faster magazines to advance in, though it's still RNG. Honey is one of those things that is either giving you honey almost every few stumps or not for 20+ stumps. It's the worst case of RNG I think I've seen for anything in this game. The short of it is that you should chop stumps every single time you see one as you play, at least until you're mid game and have enough defense against debuffs and have enough honey and other anti-infection meds. Also, there is a decent chance to get honey as a quest reward if you absolutely need it, or to find it at a trader to purchase (especially from Jen).
In short, yes, it can be annoying. I spent half a day on day 1 (on 2 hours days) running around trying to get honey to cure an infection I got from the first time I was attacked and then was so far behind in food and water from all that running that it took me a while to get back to normal. But when it comes down to it, it is easy to overcome that. Decent armor, looting medical stuff, doing quests, chopping stumps always and not just when you're infected.... there are so many ways to overcome it that it really shouldn't be a problem.