I was in the same boat and I am looking myself. I am not the most knowledgeable on the forum by any means, but I'll try to answer. The best advice I can give you is get to your local bike shop and get fitted. A tt bike is a road specific bike which is used exclusively for distance cycling. A tri bike is specific for triathlons because the geometry meaning how you sit is than that a of a tt bike. Triathlon bikes ease the power required by your quads as they are needed for the run as well. Also tri bikes tend to be more aero dynamic. Where they gain aero and power needed they lose on the ability to climb. Both are good choices. As for fit again check your bike shop. Your local bike shop may have 2nd bikes available. Also ebay is ok to try but you always must be careful. Good luck on your search and your race.

No problem glad to help. Even if you had a bike would probably be tough considering all the snow you've had over the last day or two.

I'm not sure there is a difference between a TT bike and triathlon bike. For example, the Cervelo P3 Carbon is used by riders in the Tour de France in time trials and also by lots of triathletes. The only possible difference that I can think of is that there might be some different rules between cycling and triathlon and that some bikes might only meet the requirements of one and not the other. If so, my guess is that this is oversight on the manufacturer's part.

Regarding a first bike purchase, you can learn a lot by doing research on the web. There are websites that will show you how to measure your body and how those measurements translate into a proper bike fit. This can be very helpful if you want to buy a used bike. Otherwise, going to a good bike shop is always a good idea so that they can make sure the bike fits properly. Even if you do go to a bike shop, I would still suggest that you do a lot of research because sometimes people at the shop make mistakes or they might even want to steer you into a bike for which they don't have your correct size.

TT bikes and Tri bikes can be one and the same. As pointed out above, the P3c is heavily used as a TT bike, so are most of the larger brand's tri bikes. The only time there really is any difference is if the bike uses very slack traditional geometry (seat post around 72 degrees) whereas it is commonly accpeted that tri specific geometry has a steeper seat post angle (typically 76 degrees.) Traditional geometry bikes TT bikes are getting more and more rare.