The only time I had a high FSH level was before my hysterectomy. I had one ovary left (other removed 3yrs prior) before my hysterectomy.
I had a full hysterectomy about 1.5yrs ago. I am on the vivelle patch. I couldn't tell you what my FSH levels are now, I have never had them tested since the one time they were high.
FSH is high after menopause and low in the reproductive years. For the most part, it has an inverse relationship to estrogen level. Since you do not have ovaries and do not take estrogen, it makes sense that your FSH is high.
I also do not have ovaries but I take estrogen. When my estrogen level gets rather high, my FSH is low (in the range of a menstruating woman). When my estrogen is on the lower side, my FSH rises.