Hi Charlotte,
I had cervical length checks every two weeks from 16 weeks to 24 weeks, and they often showed a significant amount of funneling (as much as 2cm). My drs never seemed that bothered about the funneling, only caring about the length, I was consistently over 3cm so they didn't do a cerclage. Period type pain is a daily thing for me too.
with 3.7cm you shouldn't have too much to worry about, likely the specialist will be more concerned with your cramping.
You can ask about a pessary since that doesn't have the same gestational restrictions as a cerclage, also progesterone too, but I think it is reasonable to expect them to not take any action at this point beyond regular monitoring. Definitely take it easy as long as you are having the cramping.
Good luck :-)