It's definitely worth pursuing with a good doctor. When I was first searching, I spoke with a doctor who said menopause wouldn't cause you to feel 'sick,' rather, just tired and lacking energy. I knew that wasn't completely true since I had a friend who was very sick when she went into menopause - stomach cramping and migraines. She went on hormones for a limited time and was fine.
So, I kept searching and found a doctor I like. I went through all the testing and am now on the bioidenticals. He also put me on a drug for thyroid since my number was on the lower end of the scale (not out of range, but low). My hot-flashes have decreased significantly and I'm feeling better overall. My theory is if I can get this in check, not only will it make me feel better, but my body will be able to better fight the Lyme. The more I've learned about all this, the more I think hormone and thyroid imbalance is a real epidemic - for women both in perimenopause and postmenopause (I fall into the latter.)