Dear Zoe, From the description you give of the rash, and that you also have it on other parts of your body would be more likely something like eczema, or perhaps an allergic type reaction.
Inflammatory breast cancer (IBC) is a serious type of breast cancer however it is rare and accounts for only 1 to 4 percent of all breast cancers. It is called inflammatory because the first symptoms are usually a redness and warmth in the skin of the breast, often without a distinct lump. It will often be mistaken for a simple infection and be treated with antibiotics. IBC would not get better on the antibiotics, however it also wouldn’t get worse. That’s what leads to the suspicion of the possibility of cancer. An infection will either get better or worse within a week or two, it rarely stays the same. If there was no change the doctor should perform a biopsy of the underlying tissue.
In many local communities there is access to health services free of charge or a small fee for persons without income or insurance. Check with your local department of health to see if there are services available to you, at least to have this rash looked at.