Welcome to Connect, @gphetteplace
You have brought something up that I never knew but that may be affecting me also! I googled sirolimus and that too can cause nocturia. I take sirolimus as my immunosuppressant after a liver transplant and I also have nocturia. No one ever suggested that the immunosuppressant could cause that, I assumed it was just typical incontinence. I also find that even when I stop drinking early, the urine tends to come out during the night. One doctor offered an explanation for that -- when you are upright during the day the fluid goes down due to gravity but when you are prone it moves up within your body. Sounds plausible.
I have had Botox two times for incontinence and it has helped a little bit. Unfortunately having Botox for incontinence very often causes a UTI too and both times that has happened to me. The urogynecologist gave me an antibiotic to take for four days, starting with the day of the injections, to try to ward off a UTI but it didn't work, not too surprising since we are more prone to infections. I did not have any pain with the UTIs just a tingling. I wonder if that's because the Botox numbs the nerves, I plan to ask the urogynecologist about that.
I am 3.5 years beyond my transplant so if my incontinence is from sirolimus I would have to say it does not go away. It is possible though that mine is simple incontinence from other causes. I hope that yours will go away, I know too well how much getting up a lot at night affects you, it is very disruptive to your sleep. I often find I need a nap during the day.
JK