My 2 year old toddler just this past week started getting red spots that look like mosquito bites(they arent).  She gets one spot flaring up at a time.  It will start to fade a bit, look less angry, and then we will check her and find another one, either on her face or back.  Has only been about 6 in all over a 5 day period, and they dont seem to bother her at all.  Havent changed soaps/food, or anything like that.  Have no idea what to make of it, or if it is worth a trip to see a doctor?  She did run a fever for one day last week, and she has a new tooth that JUST broke through, probably ion the last 24 hours.
Red spots can be due to umpteen reasons, including allergies, which you seem to have already taken into account. Other causes include contact allergy, viruses, bacterial skin infections, blood spots due to platelet deficiency, etc. A visit to her doctor is definitely worth it - but you should do it when the spots are actually visible. Just do one thing at home