Ok so I'm still playing with that same character, he's now 30 days old and the solution was quite simple and I feel stupid now. Also a friend of mine had the same "problem". It's only an INFECTION, I think me and my friend got it from getting hit by zombies while bleeding, it can happen and it sucks. Just get yourself a supply of 10+ meats (because you will lose a lot o blood) and rush to the nearest hospital in the hopes that you can find one of the rarest items in the game: Antibiotics. I myself found 2 in the hospital at Berezino, talk about luck. Hope it helps. Good luck everyone! My character wasn't coughing at all, that's why I couldn't find any plausible solution. But yes it was an infection even tho there was no symptoms.