LOL!! That's exactly what I did. I wore my hair long for about 12 years then decided to shave it down to the skin 5 1/2 years ago. I've kept it that way because I'm convinced that I look better without hair.
Since this is your first time shaving, I'd wait 2-3 days before shaving again. I remember my first time was uncomfortable but it will get easier as your scalp toughens. As for care, I'd definitely use sunscreen on your scalp for awhile. Also, I use Gold Bond medicated lotion after I shave each time. It will keep your scalp healthy. If I'm forced to use a razor that isn't as sharp as I would like, I run ice over my scalp after I shave, then use the GBML.
As for the perception that you might be a skinhead, I don't think that is a problem. Unless you have a copious amont of tattoos and hang in packs of other bald guys ( and you are white, which I'm assuming but don't know ), shaved heads are common enough these days, especially among current/ex athletes .
Welcome to the club. Bald is BEAUTIFUL!