I had digestive problems while taking oral HRT, I think it is a common side effect. Like Hurdity, I would suggest trying a transdermal HRT if it continues, they have fewer side effects and generally work better. I have Gilbert Syndrome which was definitely aggravated by oral HRT but since switching to the transdermal gel, blood tests have revealed that the GS has improved and also my cholesterol has reduced significantly.
In the meantime and while you decide what to do next, you might want to try taking magnesium tablets every day, they can be very effective and help the overall digestive system, including constipation.