Just GO. Melanoma is serious and warrants immediate attention. Call your gp tomorrow and see what he says. Melanomas are identified by the abcd's (asymmetry, b-irregular borders, c-different colors, d-diameter >7mm).
Derm or GP. That would depend on your insurance coverage. If you belong to a HMO, then you will need to see your GP first, who can see if the growth is suspicious and refer you to the appropriate specialist (surgeon or dermatologist). Melanomas require large and wide excisions, and going this route may be more practical. If you have a PPO or Medicare, you can go straight to the specialist.
Opinions may differ. If the suspected lesion is large enough, you might need to go a surgeon to get enough biopsy or do a proper excision. Changes in size, border, color, ulceration or bleeding are signs of melanoma. Early detection is vital for prolonged survival and cure. Fair skin, exposure to sun light, family history and tanning are risk factors are risk factors.