An endocrinologist is a doctor that specializes in the endocrine system (sorry, that's probably obvious...). Some endo's specialize in diabetes, some in hormones, some in metabolism, etc., and some 'do it all'.
Just a couple points to consider... First, I believe that the higher than normal LH/FSH ratio is indicative of PCOS, and thyroid problems are also common in women with PCOS.
Second, many doctors are using a reference range for TSH that's far too wide to catch many who might be affected by hypothyroidism. It sounds like the range your OBGYN is using is more current, which is good.
If it were me, I would spend lots of time reading up on the symptoms of hypothyroidism (as well as PCOS, if you haven't already), weigh my symptoms against those and go from there when deciding to pursue treatment or further testing. It will kind of depend on if you want to take charge of your healthcare or if you prefer to put your trust in your doctor. I tend to be naturally suspicious and I don't trust doctors so I take the former approach, but you should do what is most comfortable for you.
A good place to start thyroid research is
http://thyroid.about.com There are tons of links and tons of information there, and it should help you make a decision on what you want to do next.
One thing you might want to know is that endo's tend to base treatment more off test results than how you're feeling, and some endo's are still using the 'old' TSH reference ranges, which could cause you to be undertreated or even to go undiagnosed. I have subclinical hypothyroidism and had to seek out a doctor that would treat it, but I can tell you that I have improved 110% since I started treatment. My TSH was only 2.28 when I started treatment and I feel great now at .48, but a lot of doctors wouldn't have wanted to touch me with a TSH level that was in range.
If you decide you want to try meds for your thyroid, after reading as much as you can about it, I'd probably start with your OBGYN before trying another doc or an endo.