Not so much to the AC as what's in the AC. If you have an allergy and you have that allergen present in your AC, then your AC is circulating that allergen around. That applies to mold, dust mites, pollen, etc.
Patients with allergies and/or asthma are recommended to have AC in their homes. However, if you believe that your AC is causing more problems than good, you should get it cleaned by a professional. You can also look into an allergen filter system if the problem doesn't improve.
*ahem* If you've got a problem with me, just come out and say it.
But it sounds like your air conditioner needs to be cleaned out. There could be some mold in there you are allergic to. And as much as I hate the noise of my window unit, I would much rather have it on than off in the summer.
Speaking of AC's, does anyone know if the Disney resorts are still doing that "energy efficient" thing, where the unit shuts off automatically if it doesn't sense any movement in the room, and then you wake up in a puddle of sweat?