Hello,
Underarm itching can be due to fungal infection, intertrigo, dermatitis (atopic, contact, allergic), heat rash or excessive sweating causing sweat dermatitis.
You may try calamine lotion on the rash. You should also maintain hygiene and try to keep the area clean and dry, wear loose-fitting cotton clothing. Also use an antibacterial soap or mild soap like dove.Avoid deodorant / cosmetics.
If the rash persists then it will be best to get it evaluated from a dermatologist. For the itching you can take some antihistaminic like Benadryl or Claritin.
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.