I have had this happen to me. It stopped when I started using anti-bacterial soap to wash with and using a good razor to shave with and only using each blade once. They were very painful!! Try getting some anti-bacterial body wash like Dial (read to make sure it's got an anti-bacterial component) and invest in a better razor (disposables are harsh) I actually tried my husbands razor with a fresh blade and it's been so much better. (Gillette Fusion)
When the abscesses happen try wetting a washcloth and putting it in the microwave to warm it a bit and put the warm compresses on the site. That will help to bring the abscess to a head and allow it to rupture. Don't squeeze it, cover it and allow it to drain on it's own. You can put Neosporin or and antibacterial ointment on it, Vaseline is bad, it allows germs to breed. There is also a product called Boil Eaze that has Benzocaine in it to help with the pain. Don't make it too hot or you will burn your underarm. You can also try using a spray deodorant to avoid re-contamination from the stick deodorants. Once it's healed you can switch back to the Secret Clinical Strength. If they continue to come back have it checked by a doctor, he/she can culture it to find out what is causing the problem.