I was extremely dizzy on Premarin, Lil. It does list it as one of the side effects and when I popped over to Hystersisters where a lot of ladies use it I found that for those who get it, unfortunately it doesn't seem to settle.
I think you should have a chat with your GP about it and see if you can change to oral estradiol/utrogestan which I posted about to you earlier.
Hugs,
Tempest xxxx