What does small red dots on top of foot mean?

Depends: It could be something called petechial (small spots of blood under the skin). It can be due to extensive swelling, heart or circulation problems, infection. It also could be a type of rash. You should get it checked out by a podiatrist.

Usually allergy: Most commonly an allergy to shoes or socks or laundry detergent or soap. There are other possible causes and if they've been around for a while need to see your doctor.