Thank you both for replying, it's good to hear that I'm not crazy and that I should indeed be treating this as a serious bite. It really is easy to shrug it off and say "meh, just a bug bite, it'll heal," and the next thing you know your limbs/digits are succumbing to necrosis.
Yes, it's quite warm compared to the rest of my skin, and it seems to have a pulse every once in a while.
Hopefully the local doc-in-the-box is available tomorrow. I will most definitely be paying a visit, and if not tomorrow, then certainly Monday.