If you are considering patches or shots, by all means ask your doctor. My Endocrinologist was very open about which method I preferred. He asked me for my preference, and I said "It is sublingual" and he said "Fine, that works as well as any other method." He then wrote me a prescription for Estradiol and I was on my way.
Since you have only been taking HRT for 3 months now, you are most likely still producing Testosterone. If you need to have the effects of Testosterone reduced, then a T blocker, such as Spironolactone, is indicated. One caution though. Spironolactone has many side effects that are not easy to live with. There are other options. Just ask your doctor.
Finasteride is a medicine blocks the conversion of Testosterone into Dihydrotestosterone which is 20 times more powerful than Testosterone. DHT primarily affects scalp hair and your prostate gland. If you are losing your scalp hair, you need to block DHT and Finasteride is indicated.