You definitely need to let your doctor know about the other symptoms you are experiencing. Even if it's not MS, it could be something else serious, or something easy your doctor can fix (hopefully that is the case).
Everyone with MS has different symptoms and experiences, so you can't go just off of symptoms. Sometimes symptoms are constant, but for me they do come and go. If you can get to see a neurologist they will have a much better idea of what to look for.
As far as the RLS goes, I have neuropathy in my left leg (pins and needles, tingling), and sometimes I do get that restless leg feeling in that leg which gets worse at night. If I only told my doctor about that symptom, I would be dx with RLS, but since my doctor knows all my symptoms and has tests to back it up, the restless leg feeling is actually attributed to my MS dx. It's easy to get misdiagnosed when only concentrating on one symptom, something like MS requires a full picture.
P.S. I have been officially diagnosed with MS, and I still feel like a hypochondriac, so I hope that's normal. :)
Be joyful in hope, patient in affliction, faithful in prayer (Romans 12:12).