There are headache specialist who can make a more precise diagnosis. There are many different kinds of headaches and they respond to different medications. It's good to stay informed and be careful, but that is not enough in this case, so I suggest that you seek out a headaches specialist.
If it were me I would probably continue taking the klonopin (for a short period) and get myself into some good psychotherapy to help address underlying issues. (Unless the anxiety is a result of a medication issue which one could perhaps expect to resolve itself with good treatment planning and management.)
I personally wouldn't consider taking any other psychiatric med (unless it was indicated for another psych disorder, like bipolar for example).
Headaches can be a challenge. If you are able to identify the trigger then that could help you better manage them. For example, if stress or certain foods brings them on then you could either try some relaxation exercises or avoid or limit consumption of certain foods.
I would also suggest you discuss the headaches with your doctor. I've had to do the same thing myself. I actually went up to the hospital last week and they thought I had either had a migraine or had had a 'mini stroke'. Scary stuff.
Headaches can be debilitating so I would definitely get them checked out.
Just as an aside, my mother has been concussed several times (on top of having head injuries) and her doctor prescribed an anti-psychotic for that. She was unhappy taking an anti-psychotic so she was given paramax (that's probably pain and anti-nausea medicine). It could be another option.
Talk to your doctor and see what they suggest/ recommend.