in the beginning of menopause you are still ovulating just less often so yes you can still get pregnantThere is a rare condition where a person is allergic to ejaculate. You've had a lot of other problems, so I doubt that's it, but if your current gyn isn't getting to the bottom of why it would hurt to be ejaculated into, then change doctors! Maybe you are still too thin and fragile in your tissue down there. I will say that the vaginal insert estradial works as well as anything and is supposed to be safe. Be sure your doc isn't just an ob, because they do not stay current on hormone therapy, according to my primary care doctor who cautioned me about using one for gyn. What I do is call the nurse and have them call back and ask if the doctor stays current on hormone therapy, attends conferences, online instruction, etc. Or you can google and insert "hormone therapy" into your search for a doctor because some specialize.
Meanwhile, if intercourse hurts, don't do it. If you are in menopause, can you even still get pregnant? If not, the vasectomy is irrelevant at this point. It doesn't stop him ejaculating.
Also you don't have to be allergic to ejaculate for it to disturb the microbiome in your vagina and cause irritation or increased infections.