Oh, where do I begin? Perimenopause can be a pretty tough transition for many women. It is not only possible but probable that those symptoms are related. Patients with these complaints get a one-hour appointment in my practice to review the signs and symptoms that accompany this transition.
Riding it out is one option. Above all, make sure you optimize lifestyle, with exercise being probably the most important factor. Aerobic exercise of 45 minutes 5 days a week along with 60 minutes each week of strength training is a great goal to set.
I often recommend a book to patients: Dr. Robert Greene's Perfect Balance. It covers this transition quite well and reviews options in treatment including diet, exercise, and hormone alternatives. It was originally published in 2005, but is still one of the best I have seen.
Good luck! Things will get better!