Everybody gets freaked out about bugs in the house. If you get bites on you skin and they blow up and look really bad, it is still much more likely they started as mosquito bites that you scratched really hard, rather than spider bites.
Other possibilities of bug bites are mites, midges, "noseeums," chiggers, and bed bugs. All of these are cured the same way-- find the bugs and get rid of them via a professional pest control service.
The only exception to this is the scabies mite, which is essentially the only bug that lives under your skin. This is why scabies has to be treated with a medicated pesticide cream that will kill the mites that are living on you and laying eggs.