I can sympathize. For the last 6 years I've had way more sinus problems than Crohn's problems -- and I'm not even on Remicade (or Humira). I, and my doctor, are very hesitant to put me on immunosuppressants because of my sinus issues (about 25 sinus infections and 4 surgeries in a 4 year period).
Are your respiratory infections primarily bacterial sinus infections? Or do they sometimes (or often) involve the lungs?
If they're involving your lungs, I don't have much to suggest. But if they're sinus infections, you might be able to do some things to help.
How often have you taken antibiotics for sinus infections? What antibiotics have you taken?
You mentioned sinus surgery. When did you have it and what exactly did they do in the surgery?
Are you taking a steroid nasal spray like Flonase or Rhinocort every day?
Have you tried daily sinus saline rinses? After my 3rd sinus surgery I started doing these three times a day and they made a world of difference. I haven't had an infection since, though I do still have lots of drainage.
Maybe with some of these tricks you can stay on the Remicade for your Crohn's but avoid, or at least minimize, the sinus infections that seem to result from your immune suppression.