How can I fight being separated for failing BLC after refusing to go because of migraines, and then being forced to attend anyways?

If you are Regular Army, as an E4 you’ll be separated at 8 years of active service regardless because of RCP. My response to your question is to go see legal and get professional counsel. But as far as I know you shouldn’t be barred from reenlistment as an E4 for BLC because it’s not a required PME for your grade. You only need it for advancement to SGT.

At this point, your options are to request an exam for a medical discharge and/or going to the VA for a disability rating. Either way, there needs to be a documented history of treatments. Even if something actually happened, if it isn't documented on official forms, it never happened.
There are some chronic conditions that you can request a permanent profile for and remain in the service and possibly reenlist. Those conditions have predictable cause and effect, and the requested accommodation doesn't significantly affect your duties. Headaches that prevent you from doing your assigned tasks are not one of those conditions.

If you have an outstanding medical issue you should be on light or limited duty due to the issue and if it isn't getting better that should kick off a med board. That's how the process is supposed to go. Even if you are pushed into a course were you going to medical because of the issue? Failing the course without anything from Medical limits what the Commander can do. I would be talking to your Primary care folks and seeing if the MEB has been initiated or to see if there is enough to go that route.