Hello,
These bumps can be due to folliculitis, insect bites, allergic reaction or viral rashes. For these rashes, do not use any cosmetic products at the sites. You can apply some calamine lotion at the rash as it will help in soothing the skin. Also take some antihistaminic like Benadryl and apply a mild steroid cream on the itchy bumps.
If the symptoms persist then get an evaluation done from 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.
Did you change face wash or shampoo? DId you get a new hat? Could be an allergy to something like this.