The concerns surrounding venous thromboembolic events as a side-effect of hormone replacement therapy can mostly be traced back to one particular study known as the Women’s Health Initiative. This study was an enormous undertaking which, unfortunately, demonstrated significant adverse effects of the hormone therapies studied. As a result of this the use of hormone replacement therapy in postmenopausal cis women was dramatically reduced as the medical community began to question whether or not the therapy caused more harm than good.
Naturally, trans women have been suffering from this fall-out ever since.
What physicians seem to fail to recognize is that the study examined a very specific hormone regimen which was, arguably, outmoded at the time the study was conducted: It examined the use of conjugated equine estrogen (Premarin) with or without the use of medroxyprogesterone acetate. Neither of these drugs is regularly used for the treatment of transgender women.
The estrogen most commonly used to treat transgender women nowadays is 17β-estradiol either in pill form or in the form of a sticky patch that you apply to your skin. Esters of estrogen (e.g. estradiol valerate) are also sometimes used either in a pill form or as an intramuscular injection.
Transdermal estradiol patches are the gold standard when it comes to treating women who are at high risk of a venous thromboembolic event. It simply does not increase the risk of developing a venous thromboembolism. The only thing you should keep in mind is that patches are not always well tolerated because of the lifestyle changes required to keep them from falling off and the fact that they tend to irritate the skin.
It’s difficult to find hard numbers regarding the relative risk of venous thromboembolic events with regards to hypertension. The best I could find after an hour or so of searching was this study regarding VTE in lung cancer patients. Hypertension increased the risk by a factor of 1.8.
As far as the anti-androgen is concerned: The primary use for spironolactone for cisgender people is as an antihypertensive.
Even if the risk of thromboembolism was truly significant with modern hormone replacement therapy it wouldn’t justify what your doctor is doing to you. The fact is that mortality in the transgender community from suicide–caused in part due to the lack of access to hormone therapy–is substantial. The quality of life lost when a trans woman is denied hormone therapy is substantial. The fact that your doctor does not appear to be taking this into consideration when they weigh the risk of thromboembolism against not receiving necessary medical care is deeply concerning.
I strongly recommend that you seek a doctor who is more sensitive to your medical needs as a transgender woman.
Edit: Fixed a minor, but embarrassing, error.