Welcome to the forum.
Does this only happen when using the flash? Are there any other specific details you can give us?
The first thing that comes to mind, is that the batteries are low. Sometimes a camera will appear to freeze up when the flash batteries aren't powerful enough to recycle the flash, but not dead enough to turn it off. The camera's battery might be another culprit. Easy to check, just charge up all the batteries and see if that doesn't help. Keep in mind that batteries to get old and stop holding a charge like they do when new. Do you have another battery to test?
Another option might be the memory card. If the card isn't functioning properly, the camera may freeze up while trying to read from or write onto the memory card. Do you have a second card to test with?
As for upgrading to a full frame, the cheaper option would be to with Canon, since you already have Canon lenses and a flash. Your 18-55mm won't be compatible with a full frame camera because it's an EF-S model, but the 24-105mm will replace what the 18-55mm does for you on your T3i.
In the Canon line up, look at the 6D, the 5D mkIII or maybe an older (probably used) model like the 5D mkII. There is also the 5D (often called 'classic') but it's pretty old by today's standards.
Another option for upgrade would be a higher end APS-C (not full frame). The 70D or 7D (or what ever will replace the 7D). These would still be a significant upgrade from your current camera. Full frame is great, but if you don't shoot at high ISO, the difference isn't astronomical.
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