If a mole is malignant, would freezing it slow the spreading? Can I take a biopsy if a frozen mole is malignant? (photo)

I just went to the dermatologist with a mole that fit all ABCDE criteria. The doc froze the mole off. I asked him how he could know if the mole wasn't malignant, and then he told me he couldn't know, but a biopsy would be too expensive. (He thought I didn't have insurance.) He also told me that the mole might just be inflamed because of its location on my back under my bra. Now I'm scared that he did an fast fix based on money. He told me to come back in a month.