I had the exact same thing with both lips swollen and tiny bumps appeared on both lips (not cold sores) and a severe rash will cause tiny bumps to appear on the inside of both lips. For me, it's an allergic reaction to the sun uv rays and I'm also allergic to most sun blocks that has oxybenzone in it. The sun blocks give the exact same rash on my lips or anywhere else applied on my body. A dermatologist told me about taking anti-histamines for my allergic reaction and it keeps the allergic reaction from happening. The one thing the dermatologist forgot to mention was that anti-histamines wear off after a while. After taking Zyrtec for two years, I have now switched to Allegra from having a severe allergic reaction on every area of my body that was exposed to the sun. It used to be only my lips that would show the allergic reaction but the doctor said that the allergic reaction will get worse (appear on more areas of my body) as I get older. You've been mis-diagnosed. I would try another dermatologist.
From the symptoms it can be contact dermatitis or cold sores. It is caused due to HSV1. Pain, burning, tingling, or itching occurs at the infection site before the sores appear. Then clusters of blisters erupt which break down. You need to get some investigations like sample from the sores to identify the virus, culture analysis, Tzanck smear, antigen and antibody studies and blood sampling for antibody studies done to confirm the diagnosis. My sincere advice would be to consult a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.