At that speed you would not only want the 6.5 flex (extra stiff) but also potentially tipped. That is elite speed - not impossible as i have played with and fit guys at that speed, but your current shaft is for 90-105mph club speed. Go see a certified fitter as there are several other factors that go into it besides raw speed.

I'm going to guess that when you say, you've been struggling with your driver; there were times during the season that you weren't struggling with it (hopefully more often than not). If you have a current relationship with a teaching pro that knows your swing, I would start there. Personally, I'm famous for finding any reason to buy a new club. I hate it when a flaw has crept into my swing and I can't self diagnosis it. I always want to make sure I have a sound swing when going into any fitting.

Hard to imagine but the fitting saves a lot of stress and money.

What’s the problem? Hard to help without any info on what you’re struggling with. If you’re having trouble controlling your driver then it sounds like you need to slow down your swing until you learn control. You’ll hit it further and more consistently if you’re hitting the center of the face and controlling face angle at impact.