I highly recommend that you go to see your doctor
about this right away. You could see either your primary care doctor
or a dermatologist
Moles are collections of pigmented cells in the skin called melanocytes. They are usually benign, but sometimes there is a risk that they will transform into melanoma, which is a dangerous form of skin cancer. For this reason, anytime a mole begins to behave suspiciously (change in size, color, texture, etc) it needs to be examined to make sure it is not turning into a melanoma. The fact that you have recently had a bump develop under your mole and that it is now oozing is concerning to me, and I think you need to have your doctor look at it to make sure it is not a cancer.
After examining the mole closely on your arm, if your doctor is worried they will want to perform a biopsy. This is a simple office procedure in which numbing medicine is injected around the mole and the mole is removed so that it can be examined closer under a microscope, looking for evidence of cancer.
Set up a visit with your doctor as soon as possible.