Thanks for posting your query at DoctorSpring.com. I can understand your concern.
It seems to be a furuncle. It's a bacterial infection of the skin. The one that's turning purple is healing with post inflammatory hyper pigmentation.
I would recommend application of neosporin cream twice a day. Also I would recommend that you take oral antibiotics like doxycycline, you will require a prescription for that.
These medications will help in resolving the lesion.
Hope this helps, Please feel free to get back with any queries.