I think those noseeums are also called sand flies or sand fleas. Unfortunately most beaches seem to have them and yeah man do they sting when they bite.

Not to freak you out but funny story, I used to watch that show called I shoudln't be alive and very rarely they can lay eggs under your skin and cause a lot of issues. I remember watching the episode about them the night before I left for my beach vacation in Negril Jamaica and they have them bad there. It had me freaked out lol