I think that when you are on that trapeze, you are leaving so little distance between your NTH finger that you flip on and your TH finger where the string ends. If that happens the yoyo and the string hits your TH arm when you flip. Make sure that your trapeze isn’t close too the middle like you said.
Some advice:
1) Make sure the yoyo is near your NTH finger on the trapeze and not so much the middle
2)Position your “flipping” finger a few inches from the yoyo
3)PUSH into the yoyo so that it will flip without the risk of hitting your arm