Can a HSV outbreak last for 3 month? I have itchy burning bumps around mouth that seem to have spread to the nose, cheeks and neck. But Dr says acne.

Perioral dermatitis. Not herpes, which is completely different and clears in 5-10 days. The antihistamines will be of no benefit and will not reduce the itch. Beware of Benadryl: it is a sleeping pill and has been responsible for car crashes. Use of cortisone on the face, especially among young females, may cause "perioral dermatitis". It is red pimples which get worse when you first stop using cortisone. Oral minocyc.
Weeks not months. This is unlikely to be herpes. HSV outbreaks typically last for weeks, not months.