The electromagnetic field generated by headphones is miniscule and the frequencies are very low, whatever’s causing your headache is not a tiny electromagnet. Depending on the type of headphones and the volume used, however, the sound itself could be causing it, especially if you’re using some 3D spatial filter, those don’t always play well with how our brains and ears work.

Your headaches are likely because of the pressure of the headphones onto the side of your head (clamp force). The headphones might be too small for your head.

Harmless radiation or negligible amounts of magnetism will not cause headaches.

Unless I’m missing something, magnets in headphones only emit very weak, static, fields, that have 0 effect on you.

Are these open or closed backed headphones?

The closed backed ones can create a lot of pressure and hurt your ears and possibly give you a headache.

My current headphones are open backed and way more comfortable compared to my last which were closed backed.

You can hear outside sounds easier with the open backed ones though, but for me that is worth it.

Very likely to be the physical force applied by the headphones, depending on how they are worn. I cannot use certain designs because they become uncomfortable even if only worn for short periods.

Pressure and sound waves.

Its more obvious than you think

Considering MRTs use 1.5-7 Tesla, I can’t imagine microtesla will be doing anything, unless you have a piece of metal in your head. Maybe it’s an ear infection or a migraine or something like that gets worse from the cup pressure. If it’s a problem, ask a doctor.

You could easily test your theory by wearing the headphones while they’re not playing anything. Or completely disconnected.