Small purple dot next to rash, what is it? had rash for 10 days, i think it was a bug bite. what is the dot?

Tiny bruise: My guess without seeing it is that it is something called a petechiae, which is the doctor word for a very tiny bruise. Many insects inject tiny amounts of venom that can cause decreased blood clotting, and create a tiny area of bleeding like this or an outright bruised area around the bite. If more and more pop up, then need to see doc as petechiae can have other reasons to be present than bites.

Tick bite?: Do you think this might have been a tick bite? Sometimes the head will stay attached after the body comes off. This also could just be where the bite happened. Get checked to be sure you don't still have a tick head in the wound, as it can make you sick. Also you need to be sure the wound is not infected. Good luck!

Don't know: These lesions would need to be examined, a history obtained & other tests may be necessary in order to diagnose them. Usually the lesions needs to be identified to determine the solution.