Actually some fishtailing is not normal. Those arrows with that point weight at that length should work for your bow at your draw length. Might play with some different weight heads.
Also, check your brace height. If it's too low, the arrow can be hitting the riser as it passes, causing it to fishtail. It can fishtail even without hitting the riser if the brace height is too low.
Of course, it could also be a form problem. Plucking can cause fishtailing. Work on one thing at a time. Good luck.