Your eyes and skin color are very fair. I wouldn't suggest black for a hair color for you because, you will appear sickly and pale. A better choice would be a cool toned dark brown or dark ash brown. It would really showcase your skin tone and make your beautiful eyes piercing. If you're not sure, try a semi-permanent hair color that washes out after 20 washes or so. You can find those at sally's beauty supply.
To address your update, being pale can be a turn off. Unfortunately, my mind jumped to poor vampire movies at the thought, which most people are finding less and less attractive with time. I knew girls who dyed their hair black and it did seem to wash them out quite a bit, in contrast to their natural blonde or brown hair. They looked more attractive when the dye faded than at full strength, with regards to dyed color. If it looks natural, it's fine by me. It is your hair, so whatever makes you happy will demonstrate how attractive you are to others better than the contrast between your hair, eyes, and skin.
Keep the brown hair! Smile a lot and you'll be a total heartthrob ;) You have really cool eyes and all your features are proportioned well. Walk assertively, dress well, smile a lot, make good conversation, and you will have girls crawling all over you.