my whole under eye is swollen after a mosquito bite?

You may be having symptoms of an allergic reaction.  Please ask your doctor or pharmacist about taking "benadryl allergy," for instance, which is an antihistamine (it's supposed to block the histamine in the body).  Just an fyi that "benadryl allergy" may cause drowsiness, so one should *not* drive, for instance.  

Should the swelling continue and/or your vision is affected in any way, please ask a trusted person to drive you to an urgent care center or nearest emergency room.  (An urgent care center may need the patient to call from the parking lot before entering the facility.)

You don't need to worry at this point.  You're having a slightly bigger allergic reaction.  Like other mosquito bites, this one should go away on its own.  You can put an ice pack on the area to help reduce the swelling and or VERY carefully, put some anti-itch cream like Cortaid on the area -- just don't get any into you eye.  You could also try taking an over-the-counter allergy medication like Zyrtec, Claritin, or Benadryl,  This will decrease your whole body's allergic response.  

If the area gets worse or starts to hurt, do call your primary care physician.  Any bite can get infected and that when you need so see a doctor.

It is a kind of allergic reaction. Just leave it alone and try not to rub it and it should go away in a few days.