Since I was given a peri-menopause dx over 10 years ago, I believe I've had a little bit of every symptom associated with it. The menopausal symptoms can be and are everything. It would be great to get your estrogen and progesterone levels checks because it is very easy to supplement with natural hormones. Even the tiniest amount can help so much. Also, absolutely get a thyrid check because that will give you sweats and wake-ups, too.
However, I suffered 4 months of the WORST bug I've ever had this winter. I didn't get my period the entire time except for tiny spots. The cough, sweats, urination, very low fever (with sweats and freezing) and it feels very much like the peri-menopausal symptoms I had in my late 30s combined with undx thyroid disease. They are also a lot of the symptoms I had every first trimester I had. So, my head was spinning thinking how can menopause make me feel like I have the flu. I finally got steroid from my doc that helped a great deal, but it did come back a month later.... more steroids later I felt better about 2 months ago. My af came back and has been regular 3x. I think I was so sick that I got irregular and the obvious pre/current menopausal stage I am took a turn, also.
All I can say is be alert to this horrible and strange bug that is going around. My dh has it now and it is horrible... and a little bit different in everyone. The biggest problem we both had was severe exhaustion and a little bloating, too. Very strange bug and what you describe sounds just like it. Feel better, hugs.