Sorry to hear about your injury. No, there is nothing wrong with doing cold all day. However, just be sure to give yourself breaks in between long enough to regulate your blood flow again. Cold slows it down and constant cold can cause the area to stiffen up and reduced blood
Once you start the BFST, a 20 minute treatment stimulates the blood flow for a good 3-4 hours afterwards. Doing one treatment every 4 hours is sufficient to get optimal blood flow throughout the day. If you want to do more, that is fine but if you ever feel discomfort, that is a sign you are over doing it. More treatments do not necessarily mean quicker healing. You need to condition your wrist to get used to the promoted blood flow. I would recommend starting slowly and building yourself up.
In terms of how to tape, I would recommend going to YouTube and search how to tape TFCC injuries as there are many ways to tape the area. Do what works for you.
As for other tips, just try to rest and really listen to your body. Any time you are in more pain than normal, go back to the cold when needed. When feeling better, keep a routine of the BFST. When doing PT, you may benefit from a BFST treatment before and be sure to put cold on after.
If you have any further questions, please let us know. We wish you all the best in your recovery.