Hi-
it sounds like two seperate things to me, the tightening after sex is your uterus contacting a bit- same as braxton hicks- I get that really badly with this pregnancy- with my first, I never did. It can be pretty intense and it can make you feel like you really need to pee imediately, and then you go though all the discomfort of getting dressed, and getting to the loo, only to pass a teaspoon full of pee !!!!!
The pain going up the stair etc is probably round ligament pain, from the lower abdominal muscles supporting your bump. This comes and goes thoughout pregnancy- especially around times where you notice your bump is growing- the muscles have to stretch at your uterus grows.
It's alway worse when you are getting up from sitting or lying down, or moving quickly- the "bounce" factor of plodding up the stairs would definately cause some pain. If it's a quick stabby/dragging kind of pain, then that's definately it. The muscles will "catch up " and it'll go away for a few weeks, only to come back again when you grow again. I've heard a hot water bottle or some thing can help- but i've always found by the time i've boiled the kettle, it's gone- it's a horrible but quick twinge.
Just take it slowly- don't get up too quickly, take the stairs slow- and if you find anything that helps with the after sex crampy feeling- let me know would you? It's ruining what's left of my sex life !!!! We already have an active two and a half year old, and i'm almost 30 weeks gone now- we don't need another obstical in the bedroom !!!!!!
Take care !