It's possible that you have leishmaniasis, which is transmitted by some (not all) sandflies in Belize, Honduras and elsewhere in Central America. See below. Or it could be just a strong reaction to the bites. That's the more likely case, but it's worth having it checked. Only a doctor, preferably someone with tropical medicine training, will know for sure if it is leishmaniasis.
Here is an excerpt from my book, Guide to Mainland Belize, on the subject.
>>Some people arenít much bothered by sandflies (aka sandfleas or no-see-ums). Some are. .... Quite a few travelers go home with ugly bites. If that happens to you, see your doctor who can prescribe an ointment which usually will quickly take care of the bites. However, a more serious problem which can be caused by the bites of sandflies is leishmaniasis, a disease which may cause the skin to develop sores, leaving scars. In some cases, it can be a serious health problem. If infections from sandfly bites donít seem to heal, seek out a tropical medicine specialist.