I am egg sensitive and my lips swell up when I eat eggs. They burn too. Usually the rest of me gets hives though, and I take reactine and within a number of hours my lips feel better. After a swelling incident when they deflate (haha) the skin remains cracked and annoying, but not too painful. They do not bleed or ooze. Have you ever been tested for HSV? YOu can do a blood test or have your family doctor culture the infected looking parts. Its quick and cheap test and comes back in a few days with results.
I agree that an allergy is a possibility, or some sort of contact dermatitis.
A referral to a dermatologist can be considered at this point. If the cause continues to be unclear, an skin biopsy can be considered for a more definitive diagnosis.
There are stronger steroid creams than hydrocortisone, and that can be considered if an allergic reaction is the case.
Another consideration, especially with the drainage, is an infection. If that's the case, antibiotics would be needed.
These options should be discussed with your personal physician, or with a dermatologist.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
Kevin Pho, M.D.
KevinMD.com
Twitter.com/kevinmd