How to get rid of swelling around eye from itching allergies?

Antihistamines. Over the counter medicines like Benadryl (diphenhydramine) will help some, but you may get more relief from anti inflammatory or anti histamine eye drops. Ask a local pharmacist to suggest some that may help (something like ketotifen).
Depends on severity. May need cool compresses, avoid irritants, antihistamines, steroids, etc.
Allergy meds. You need to take your allergy medicine daily to stop you from rubbing your eyes from itching . You may apply cool compress to soothe the eye and distract you from itching sensation. You many need allergy eye drops. Please see your doctor.