Hey @tri2mum,
First of all sorry to hear you've been through this, and it is still early days and you must be feeling so many emotions at this stage.
I had a mc last month (my first also), and was in a similar situation - i have 3 sisters, 2 I speak to regularly, 1 lives in another country and we aren't close, We speak on a group thread, but rarely if ever privately message/ email/ or talk...so it felt weird telling her.
She didn't know I was pregnant, and generally I only told people who knew I was pregnant about the mc (with a few exceptions).
Although I feel mc should be more openly discussed in some ways, its also quite private and personal. It may well be when you have your next pregnancy and when you tell your sister about that pregnancy, you may want to mention your previous mc perhaps?
My friends were all great, as was DH, but my mum and the 2 sisters i did tell - both of whom i am pretty close to - were all pretty useless during the first few days, and only surfaced and offered support about 8/9 days after - by which point I felt so much better, and didn't need them to rallying round (but would've greatly appreciated it for the first few days!)
i don't know why, some have suggested perhaps its easier for friends to support you as its not as immediate to them. I don't know!
I would say telling your sister my lead to further upset as she may not give you the support you need - and say the wrong thing, or nothing at all. Or, it could go the other way and this could help you rebuild your relationship.
From my experience, I would give yourself a few days, as think about when you're feeling better.
I hope this helps xx