Hi. I am responding to a 4 year old post but perhaps you are still out there. I have had to give up swimming (after many attempts to vary my technique) for the reasons you mentioned. I also can not lift upper body weights....even yoga moves which involve a lot of turning of the head will cause migraines. I have concluded that it is due to pressures built up from swelling of the muscles and blood vessels around the neck. I very much miss these kinds of vigorous exercise and hope to someday find a solution. Have you had any luck in your efforts.
I suffered migranes after a Karting accident at the British 24hr where I hit my head (in a full face helmet) I had MRIs, Xrays etc but in the end I was given Beta-blockers for a couple of months. Ever since finishing that course of medication (over a year now) I have been migrane free (although that is the ultimate jinx)