It very likely IMO that you did mess up something under the hood, as the Tilt is a real brick compared to the lighter Nokia candybar style handsets that could really take a beating. I've only dropped my Tilt once and it was on relatively thick carpet with padding underneath.
OTOH, it is possible that they're doing work on a cell site near you- it will take a call to tech support to get them to address the issue. If you don't call and complain, nothing will likely happen.
Before bothering with this step though, as we aren't 100% certain you've damaged your Tilt, I suggest borrowing a friend's ATT 3G handset (any brand will do) and test the signal out with your SIM using their phone in the locations you've complaining about. This will likely give you the best indication of what's going on and eliminate some things.
I got a Motorola Q9h last month and signed up for AT&T when I did. Before then I was using an AT&T Tilt on T-Mobile, and reception was terrible then too. AT&T was amazing for about a month, I had full 3G everywhere, even elevators and old Philadelphia buildings. After about a month, the reception is only good when I'm outside or near my window, and reception in building is full EDGE at best.
I drop my phone a lot, could I have damaged the radio by doing so? Does anyone know if AT&T gives you great reception for the first month and then doesn't afterwards? Has anyone had a similar experience?