Brief Answer:
Local care / antibiotics and multivitamins.

Detailed Answer:
Hi.
Thanks for your query and an elucidate history.

This is a condition looks to be Hidradenitis in which the sweat glands of the armpits become too much sensitive and secrete more than the normal. During this stage the ducts of may glands get blocked to have the problems you are facing.

I would advise in such a patient the following:
Get the blood tests particularly sugar to rule out any diabetes.
If pus formation is there, you can get the gram staining and culture and sensitivity tests done, this helps to select a proper antibiotic.
Once the sample is sent you will be started on a course of an antibiotic.
Also take Anti-oxidants in the form of multivitamins.

Local cleaning of the area with plain water at least three times a day help a lot for local cleaning and reducing the chances of infection. Keep the area dry with a hair dryer after cleaning and then apply Povidone iodine liquid. Let it dry.

Stop using any local applications / ointments.

You can use / apply liquid Povidone Iodine 2 to 4 times in a day, starting with at bedtime and the first thing you get up in the morning, before going to work and the moment you come home. This helps to sanitize the area.

Consult a General Surgeon so that he can inspect, palpate to confirm the clinical diagnosis, advise you the relevant tests and prescribe you antibiotics and supportive medicines.

If the medical line of treatment fails, we still have the option to get the disease bearing skin excised and use plastic surgery techniques to cover the defect. Since the skin bearing the diseased part is removed the cure if permanent. But remember this is the last option.

I hope this answer helps you to get treated well and get a cure.
Please feel free to ask for more if you need to or if you feel there is a gap-of-communication.

---