I can't help with the hrt as I can't take it due to family history of breast cancer. I can totally understand your desire for a scan and blood test, what you need to think about is if and I know its highly unlikely but if the scan/blood test showed up anything of concern then they inform your Gp who then has to refer you on nhs which can all take time. Unless you can afford to have private treatment this I have found can be the downside of having private tests.
Have you actually told your Gp how worried you are and how much an ultrasound would put your mind at rest?? My Dr always says he is not a mind reader and if I am worried about something not matter how silly I think it is then tell him and he can explain why he thinks I am wrong or arrange a test to allay my fears.
Also to consider, is it worth the anxiety etc to continue with hrt? Its about quality of life, was your life better before than it is now or not?
Someone with lots of experience of hrt will I am sure post a reply very soon, but I do understand your anxiety x