In general, bio-identical estradiol especially non-orally, which you are taking, appears to have few side-effects and many benefits in women (cis or trans and even men who take high doses for prostate cancer), based on studies. One study even found a high dose of patches appeared to protect against the risk of thrombosis and seemed to improve cardiovascular (lipid) markers in men aged 49-91 yrs old. So this is promising indeed. Breast cancer is rare in transwomen and does not appear to increase due to HRT in our population, also promising. Exclusive use of bio-identical estradiol has also never been associated with the onset of a prolactinoma in transwomen, a rare benign tumor of the pituitary gland, reported (perhaps under-reported) only 8 times in the literature, often with the use of an anti-androgen called cyproterone acetate, not FDA approved.
Finasteride can apparently have adverse effects on mood (depression, anxiety) in a few people although personally, I don't think I had any such symptoms when taking it and I have personally never come across any that did. Still, the risk remains, even after discontinuation, it appears. Other side-effects include sexual dysfunction such as erectile problem, ejaculation but these are expected and even desired for us. Another is osteoporosis but estrogen usually prevents this. It was also found finasteride could lead to a reduced incidence of prostate cancer but a higher proportion of high grade prostate cancer.
Note that this anti-androgen only reduces DHT (dihydrotestosterone) levels, unlike other anti-androgens which have a wider and more potent action (blocks and/or reduces androgen). BUT, estrogen also reduces testicular production of androgens and limits its action also by increasing SHBG levels and having certain intracellular effects whereby tissues may become less sensitive to the actions of androgens.
I'm not a doctor though and I am just reporting what I read in the literature. Your doctor should be able to inform you in more depth and as long as you are in good hands, I don't think you should be concerned.
Have a great time being YOU! Best of luck.