They do sound like bites. Spider bites are a possibility, but it doesn't matter that much. Treatment for such bites is just keep them clean and to apply an antibiotic ointment like bacitracin or neosporin twice a day. By this point, systemic toxicity--which isn't very common anyway, even with spider bites--does not seem to be a concern.
Please see a doctor in person to confirm these impressions. In cases like yours, diagnoses cannot be established by internet research.
Best.
Dr. Rockoff
Been there, doing it.
FixitGuy