They may well be flea bites - sorry. You are right, you could well have brought them into the house on your clothing. However, flea bites tend to be around the lower legs as the fleas usually are on carpets. However, could well be gnat bites as these often come in clusters on and can be quite nasty. Give your rooms a good spray with insect killer and leave the door shut. That should take care of gnats. Flea treatment sprays for the home would also be a good idea. I know midges bite, but don't know much about how they look.