Sorry, but it’s a common misconception that remission means you should feel completely better.
That may be true for some - especially in the relatively early stages of the disease - but is not the reality for many.
I often describe it as if I’ve always got flu’, and watching some of the MS Soc. videos about fatigue the other day, I saw another lady who described it exactly the same way. “Jetlag” and “hangover” are other popular descriptions I relate to.
I’m not on DMDs myself, but I do know they only set out to reduce frequency and severity of relapses, not treat symptoms. So unless your feeling groggy all the time is due to relapsing a lot, I don’t think you can expect to feel much better in yourself. You seem to think you’re not relapsing at the moment, so it’s unlikely DMDs would help with existing symptoms. You might ask whether there’s any other treatment that would, though.
Quite a few people are on drugs for fatigue, though I’ve never been offered any, despite spending every afternoon asleep.