After a while I got some impulse to start boiling some water, then once it started simmering I took a cup and just started pouring scalding hot water over the bug bites (not enough to actually scald, but just enough to feel the burn).
That was about 30 minutes ago and so far I feel absolutely no itching So if you ever run into the same problem as me just trying pouring hot water on yourself, maybe it'll work.