Sounds like both doctors are saying they think you're fine but are referring you for tests either to be super cautious or they think it'll give you peace of mind. Since your feelings of weakness started when you read the letter about your lack of weakness, that could tell you something :) If you had ALS or MS, you'd BE weak, not just feel weak. However, feeling weak is really common with stress and anxiety.
Once your nerve conduction test comes back all clear - which is what your doctors are expecting, and they know their stuff! - maybe ask for a referral to a mental health care professional who can help you deal with your anxiety. It sounds like it's been making you miserable for a long time, and as everyone here knows, that's not a very fun way to live.