I refuse to take any medicine not absolutely necessary in order to stay living, because I know the enormous healing power of my body and its immune system. Things like Tylenol are certainly one that you don't overuse, as you WILL get an immunity, and your body will begin to produce less pain-reducing chemicals since their appears to be enough in your blood. Your body will voluntarily shut off many production centers if it sees that it isn't necessary; serotonin is a perfect example. That said, taking antibiotics is generally not a bad course of action -- because of their nature, they actually HELP your immune system develop antibodies of its' own to fight the infection. The only thing we hurt by taking antibodiotics is humanity. Its a small case, but you are causing bacteria to breed resistant to certain antibiotics. If we continue to use large doses of penicillin, bacteria immune to penicillin will (and have) begin to develop. That's the only downside. So no, your immune system is fine.
Oh, and yes.. there's definitely a way to "never get well" -- it's called dying.