I think this goes for people going through any kind of significant life change, whether it be a health issue or a divorce or a death in the family:
Ask, don't tell. Ask how they're doing. Not in an "I'm just dying for juicy gossip, so please provide drama for me to snack on" way but in an "I'm your friend, and I care about how you're feeling" way. People can tell the difference. Listen to what their experiences, worries, and observations are. Don't cut them off half a sentence in to tell them about what your cousin's grandfather's barber's best friend's daughter did that totally cured her whatever. Don't go on about how weird and scary you find all this stuff they're dealing with, and "I could never give myself shots every day." It's not helpful.
Let them still be a person. Yes, this big, dramatic thing just happened in their life, but they're still just a human being that gets out of bed in the morning and makes goofy observations about the billboards on the freeway. Engage with them on the regular topics you normally talk about. Everyone needs time off from talking about the big, dramatic things in their life.
A week in, your friend may not be an expert about diabetes in general and her own situation in particular, but I guarantee you she knows more about it, and thinks more about it, than anyone else in the room. There's no need to question whether she's "allowed" to do this or that, or have a freakout when someone brings a platter of cupcakes to the Halloween event, or check on her health status every five minutes. She's a grownup; she's got this. Offer help when it's requested - don't chase people around the yard with it.
Be chill about whatever she needs to do that she didn't do before. Don't get exasperated if she has a five-minute conversation with the waiter to figure out what to get. Don't freak out if she pulls out a syringe or does a blood test or excuses herself for a minute. If you get food from a food truck together, don't grab your hot dog and traipse off without a glance, leaving her to stand around taking her shot by herself so she can eat her item. Be a friend.