I have a mole that is painful, black, and has a purple ring around it. My derm. is booked for 2 months. Should I wait? (Photo)

My mole changed in color and became painful very suddenly. I scheduled an appointment with my dermatologist for 2 months from now, and they felt comfortable waiting until then to look at this mole, because I have no history of melanoma. I'm in a panic, thinking it should be seen before then. I called around and can see a new dermatologist in one month. Is it safe to wait a month or two? No one was willing to expedite the process. How much worse can it get in a month?