Hey there
While the excess hair you have on your body, and the dark patches of skin you have are symptoms of PCOS, the only way to be sure if to check with a doctor. I wish I could help you more right now, but I honestly cannot.
In regards to the excess body hair: Several women with PCOS do have excess body hair in places such as arms, back, and face. I know it's embarrassing at times and bothers you, but if you do see your doctor and are diagnosed with PCOS, you can start to get rid of it! There are several prescription creams(Vaniqa is a popular one) that have several success stories. If you are really bothered by it and want to try something out now, I have some friends who have tried hair bleaching(you can buy some of this from any pharmacy store, or Target.)
About talking with your mom, maybe you should print out some articles on PCOS or show them to her from your computer. Educate yourself first, and plan out what to say. Show her your problems, then what it says about that problem online. I think with some parents, they will take the facts more seriously than simply their daughter complaining of body hair.
Sorry I couldn't help you any more, but just relax. There are ways to fix these problems! Good luck!