Do you mean your menstrual cycle? Is it unusually short, like 21 days? I am not on meds, but I've found it curious that I went from 30-33 day cycles to <24 days in the last year, the same time I've been having odd physical symptoms that are likely related to my thyroid.
Certainly an interesting idea though.
My own experience with levothyroxine-no change. However I'm also on birth control.
My cycle was every 29 days, without fail, prior to meds. Now? Maybe every 26, 27, 28...but never 29. Weird, but there it is.