Persistent Red Bumps On The Arm And Face Of Toddler, Used Pimple Gel, Have Dog In The House. Suggestions?

My 20 month toddler has had a random red bump on her arm for atleast two weeks now. I put some pimple gel on it once last week, and it seemed to help, but i didnt keep it up. Now she has 3 random bumps on her face (3 days old) and the one on her arm looks just as bad as before. She notices that they are there, but they dont affect her more than the occassional itch . I actually had a random red bump on my arm (same exact spot as hers),and mine cleared after one treatment of pimple gel. We do have a small indoor dog, and she has been playing outside where the mosquitos roam. Just figured the one on her arm wouldve cleared by now should it have been an insect bite. The best way to describe them is a pimple with no head. We bathe her every night. No changes in diet or laundry. Any suggestions?