Near-constantly ill

I'm almost constantly ill with some low-grade infection.

I eat a healthy and balanced diet, I exercise regularly, I'm a healthy weight and yet I'm almost constantly ill.

For example, around 2 weeks ago I had to go to the doctor with a sinus infection that wouldnt clear up on its own, after 10 days of antibiotics I was feeling better but now have tonsillitus. I know these things can be related, but this happens all the time. I get tonsillitus at least twice a year (but they've refused to take my tonsils out), I'm prone to chest and sinus infections and I often have dizzy spells and headaches when I'm feeling otherwise ok.

I've been tested for lots of things because this has gone on for years, but nothing has ever come up.

Does anyone know what can cause this? I'm at my wits end at the moment, I've just started a new job, they sent me home when I had my sinus infection because - in their words - I looked like I was dying, and now I'm at work with tonsillitus because I cant face the thought of calling in sick again when I'm so new.