Hello from JustAnswer.
If there is a red streak extending from a boil, then that is concerning that the infection is getting worse, and ill likely need oral antibiotics. A boil also will frequently need to be drained to facilitate healing. A skin rash also can develop from an infection, but also can occur as a reaction to the topical antibiotic.
There are many reasons for a boil to form in the skin under the breast, but it is most often due to an infection of a sweat gland, follicle, or a cyst in the skin. It is also possible to get a boil in the breast tissue, itself, rather than in the skin, but the description sounds more like an infection in the skin.
Since oral antibiotic are likely necessary, it would be better for you to see your doctor.
If you can attach a picture of the boil, rash, and red streak, then I may be able to better comment upon the cause of the rash and the degree of concern about the red streak, although I realize that this is an area that is potentially embarrassing. The picture does not need to include the breast, itself, but only the boil, rash and red streak.