Anxiety can produce a wide range of symptoms and sensations and both headaches and stomachaches are reasonably common ones.

No medical workup can 100% rule out the possibility of an undetected medical problem and headaches can have many causes. However, it seems likely that his main fear is that the headache is a sign that he is having an aneurysm or other medical emergency and my understanding is that an aneurysm would be detected by a CAT scan. Since interoceptive exposure produces the headache, this provides additional evidence that the headaches have mundane causes rather than being signs of a medical emergency.

On the question of whether his headaches can be expected to "peak and pass," yes, almost all headaches peak and pass eventually. However, that can take a while and headaches can be very uncomfortable until they do pass.

The question of whether using pain medication is inconsistent with acceptance or not is a tricky one. If his basic mindset is "This headache is terribly dangerous! I have to make it go away!" then using pain medication would be inconsistent with acceptance and would be likely to reinforce his fear of headaches. If his basic mindset is "Headaches are unpleasant events that happen from time to time, let me do what I can to cope with it until it passes," then taking Tylenol or another medication as one part of coping with the headache probably would not be a problem. However, the distinction between coping with the headache vs. desperately trying to make the headache go away can be a subtle one.

I hope this is helpful.