Well, that's good. Doesn't sound like a blood clot, either.
I'm not sure that symptoms occurring the next day would be related, but dehydration can cause light-headedness/fainting when having blood drawn; the effects are often experienced immediately after. Dehydration can also make for difficult phlebotomy.
I saw the room spin the first time I had blood drawn. From that time on, I've always made a point to load up on fluids prior, and I've never had any problem since.