Is this a bedbug bite/Do we have bedbugs?

Well, they really don't look like bug bites, if they start poking out then it might be, usually bug bites poke out. If you have a pharmacy around the area or someone you can ask, that might be helpfull. I had bug bites befor and they was itchy and annoying. You can do more research and find out more, im just telling you from experiance. Best wishes.