Do I have a bee sting infection? Been 3 days and still itches a lot. Is turning purple and sting site is whiteish and slightly raised. Also warmer.

Bell venom allergy. It's much more likely that you're allergic to the venom the bee injected into you. Itching is a hallmark of allergy - and if the area is inflamed like that, it's probably all allergy. I would try putting some ice on it (10 min on, 10 min off), take some benadryl or other antihistamine every 6 to 8 hours and see what happens. If you develop a fever, or the rash area extends, you need to show a doc.