Generic meds...refusing and going with name brand?

I switched pharmacies because of my location. The new pharmacy carries the same generic drug for one of my medications, but it's from a different manufacturer. They do not have the same generic manufacturer that I was taking.

My prescription is for the name brand and is allowed to be replaced by a generic. And, after just over a week of taking this other generic med, I'm having headaches that are not typical. I was on the first generic for 3 years without changes the whole time.

If I tell the Rx that I need the name brand, what is the outcome financially and with insurance costs? I know it will be higher...but if you have any insight on what I might be looking at, l would appreciate it! Thx!!