If it' s a dual cam bow and the string creeped(stretched), it should creep equally and not cause not movement.

If it' s a single cam bow, and the string creeped, the nock should have dropped, not rised. There is more string above the nock than below the nock and when creeping(stretching) the nock will drop.

You could check nock movement if your serving or nockset wasn' t tight. Also check center shot. If you have a recommened local pro shop, it might not hurt to give them a visit.

Check your rest for tightness, over the years, I' ve seen rests drop, prongs move etc...

Curious to why you don' t know the make/model of your Hoyt...single cam, dual cam...?