There are two possibilities.
1 You are reacting to the caffeine in the tea or coffee.
This can be tested by Dr. Coca's Pulse Test.
There's a long version (free download) which takes a week to complete and there's an short version which almost instant (albeit not as precise perhaps).
Here is the short version:
Just sit in a chair and come to rest for about 5 minutes. Take your pulse for a full 1 minute (not the 15 sec. multiply by 4 thing). Then put whatever you want to test in your mouth and chew it for 30 seconds. If it's liquid I would swish it for the same amount of time in my mouth.
Then take your pulse again. If you find it is faster by 6 beats, you are allergic or have a sensitivity to it. If you have type “O” blood, use 4 beats as the criteria instead of 6. It’s that simple.
2. You cannot tolerate hot drinks.
How about when you are having a nice hot soup? That will be one easy way to test.
Another option is to make a cold/ice coffee, like cafe frappe or cafe fredo and see if you react the same.
I hope this helps,
Niko