I think it’s very likely to be caused by the MS - although I realise that’s not quite the same as being sure. But in situations like this, I tend to look at what is most likely. Is it a rather unusual symptom for MS (and therefore more likely to be unrelated), or rather typical? In this case, I’d say rather typical, so do you really need to rack your brains (or badger your doctor) for an alternative explanation?
If the diazepam has helped, it certainly suggests it’s muscular, as you’d already guessed, as diazepam is a muscle relaxant - which would lend weight to the theory it’s all connected with the MS. If an undiagnosed person had muscle spasms, I wouldn’t automatically assume they had MS, but if a diagnosed person has them, I’d think it’s almost certainly connected.
Diazepam is fairly commonly used to treat muscle spasms - in both MS and other conditions, so yes, I think it’s a reasonable option. It can be combined with ordinary painkillers, and also with other types of muscle relaxant (e.g. Baclofen), if it isn’t fully effective by itself. Although there may be no 100% effective treatment - it may be a case of easing it as much as you can, and living with the rest.
Although many people with MS are intolerant of heat, I find a hot bath tends to ease muscular pain - at least for a while.
Don’t know if this is something you might consider, or if you know hot baths make you worse. I definitely get more muscle problems in general if I allow myself to get cold (all too common, at this time of year).