There are two very different arthropods in these photos and unfortunately, the quality is not good enough to get a definitive identification of either.
The first two photos appear to be a springtail, or Collembola.
During hot, dry periods in summer springtails sometimes migrate from
lawns and outdoor areas to homes. This occurs when the soils and leaf
litter where they develop dry out, forcing springtails to seek sources
of moisture, which shaded, more humid buildings provide. If springtails can find their way into a building they will usually
be found in areas where water sources are present, such
as bathrooms or kitchen sinks. Outdoors, a faucet or pooled water in a
garden is attractive.
Springtails within a home will not bite, feed on household items, nor
cause any significant damage. They can be a temporary nuisance, but
migrations usually last less than a week and springtails trapped indoors
soon die out.
For more information, check out the links below:
The other insect is more difficult to identify but may be one of the scentless plant bugs, possibly Arhyssus sp. They frequently migrate into dwellings, where they are an annoyance. Their nymphs (young) feed on plant tissues and may cause some damage to household plants but neither the adults or the nymphs harm humans or pets.
As with the possible springtails described above, it may be easiest to just vacuum up any bugs that are found inside the home.
As far as what may be causing the "red swollen bump that itches and burns", I can't say. The presence of springtails in the home does bring up a question though. Is the humidity high (i.e. above 60%) in your home? High indoor humidity can be attractive to a variety of mite species that could cause the symptoms you are describing.
In order to determine the source of your possible bites, it is nearly impossible to do via the internet. You should consider taking samples of insects in to your local county Extension office for submission and positive identification to determine the proper course of action, if any, is necessary. The local Extension office would also know if there are resources available to you to determine the cause of the symptoms you describe.
I hope you find this information helpful and wish you the best of luck.
