For anyone who's skipped to the last comment, I'll summarize what I've read on here so far (and add what I've read elsewhere, afterward):
(1) It seems that tick (and other insect) bites can last quite a while, stemming from different causes (infection, allergic reaction to the bite itself, transmission of a disease).
(2) Some of the topical applications that people have tried with some varied success are: Teatree Oil, Neosporin, and grain alcohol.
(3) It's not uncommon for a tick bite to itch for weeks, and in some cases for months.
(4) Some doctors have suggested a medical procedure to remove the "affected" area, but in some cases the itching returns (perhaps not all of the allergen was removed?).
Put simply, this does all point to a medical reality that some people will have this many-month-long reaction to tick bites (even when the entire tick is properly removed from the bite area). There are some sites that are stating that some people are so allergic to tick bites that they can go into anaphylactic shock, sending them to the emergency room.
So, it boils down to this: if you have a tick bite that has lasted more than a week, go to your doctor and get tested for "Lymes Disease" and possibly "Rocky Mountain Spotted Fever". At the very least you can start eliminating those two as possibilities. With those two out of the way, you can focus your energy on eliminating the itch, if not actually eliminating the cause.
I have three current tick bites that have been with me for over two weeks, and I've also seen bite-like, itchy areas pop up where I didn't remove any ticks. Are they related? Not sure, but I'm treating them all the same right now.
I've been applying Hydrogen Peroxide as an anti-infection precaution, and it's effective at temporary itch control. It stings like crazy when I first dab it on (especially if the bite is "open"), but I do notice that the center of the bite usually "bubbles up", signaling an open wound.
I don't think anyone is going to find a magic bullet for this issue. Prevention is probably the best bet going forward, if you have come to realize you're one of the many people who have this bad reaction to tick bites.
Looks like I'll be going to the store soon to pick up a few pair of white sweat pants so that I have something to wear when I'm working in the yard, for easy spotting of ticks crawling up my legs. <sigh>