One of the criteria for diagnosing ME/CFS is that other illnesses must be ruled out. If they haven't ruled it out, shame on your Dr.
There do seem to be a lot of similarities in the way the 2 illnesses present, especially in the early phases of illness.
Can you not just ask whether it was considered? If you are worried about looking like a hypochondriac, why not say a friend brought it up as a possibility?
I am in the same position and know the feeling of having to push for other tests.
A couple of years ago I was having problems with my foot and I explained my symtoms to my GP who said he thought it might be MS and so referred me to a neurologist.
Neuro subsequently ordered an MRI and that came back clear.
Went I went for my follow he was very brisk and when I wanted to ask some questions he got up, opened the door and said there was nothing more he could do with me and that I should stop try and find something other than ME to blame my ill health on!!
I was very upset and frustrated.
Since then I've ping ponged about with various GPs who I now rarely see.
You are so right about the treatment differences between those with ME v MS, it's really upsetting that you get no help at all from the medical profession and you can't even see a neurologist once or twice a year for a check-up and see how you are, suggest physio or new drugs etc. Even though it is classified as a neurological condition there's no neuro support!
I know they have to rule other things out before dx ME but I wasn't offered an MRI or LP before they made the dx so how could they have been sure?
Helen41 makes a good point about suggesting a friend spoke to you about it.
Good luck x