Hi Elise. I will offer you some advice below that you probably don't need, just since I don't know enough to give more technical answers. But since there are other people here who might be able to answer with higher level info, it would help if you let us know if you are running your phone in stock mode just like it came from the store/carrier or if you have rooted it and are running some other rom on it. If those terms sound foreign, the answer is that you are running stock. Either way, it may help other people answer if you list what numbered version of the operating system (whether stock or custom) you're using, which you should be able to find out from the settings menu under something like "About This Phone" (not sure how it reads because I'm running a custom rom that might be different in that area). For example, I'm running the Virtuous Unity rom v2.39.0, Android version 2.3.4, and HTC Sense version 3.0. People may be able to use that information to let you know of particular problems with your rom or version and may help them give you a solution.
Now for my Android-for-Dummies advice (best I've got):
Have you powered down the device as in shut it all the way off, taken out the battery for a bit, and restarted it? If not, try that.
Have you tried the thing in the settings menu where you tell it to check for updates? If not, try that. Maybe a pending OTA update would resolve it. (Or maybe you just got one and that's when the problem started)
Have you tried doing a factory reset? This will wipe out everything on your phone and return it to the state it was in when you first bought it and you'll have to set everything up again in terms of re-downloading your apps from your accounts at the app store(s), setting up your icons and widgets and wallpapers and screens the way you want, etc. Anything that was stored locally and not backed up to the web or to an SD card will be wiped out, such as photos and local data in some apps that don't back up to the web (maybe notes or gas mileage entries or saved game data, etc.). Obviously if you're rooted and running a custom rom, this would be a more complicated issue involving re-flashing the rom and all, but if you're not running a custom rom it doesn't apply and if you are running a custom rom then all of this advice is elementary and someone with your tech level would have already tried these steps. I'm listing them since I don't know your situation.
One thing that happened to mine for a while that may be somewhat related was that I'd get a wrong number call but it would show up as a call from my buddy, with his contact avatar showing with the unknown number. Strange. It happened for a while and went away, not sure why.
If all else fails, call Verizon support and let them know it's happening. Maybe they'll send you a replacement. They'll probably walk you through similar steps I've outlined above before getting to that point. If you do send it back, be sure to do a factory reset first so your info and accounts aren't still on it.
OK that's all I've got. Good luck!