What time of day is your vet appointment? In the past I have put our hammy in his pet carrier in the morning and let him sleep in it then taken him to the vets. You can make it nice and cosy with lots of substrate, lots of torn up white toilet paper (they tend to make another nest while in there), and a little house she can hide in. I also hide quite a few treats in the substrate and scatter some hamster food as well, plus add a piece of cucumber.
They forget to be stressed if they have some foraging to do and can bury themselves in toilet paper and hide in a house.
I also have a blanket I put over the pet carrier when it's on my knee in the car (assuming someone else is driving), so it's dark and flashing lights and noises don't bother them so much.
Our hammy just used to go to sleep in it, if cosy enough.
The pet carrier needs to be big enough to make it cosy with a little house and plenty of substrate. Not sure which one you've got but most hamster ones are far too small. I have a guinea pig sized one (the Aladino). You can just use a tissue box or something for a house. I use one of the little plastic pod houses from the Hamster Heaven, or a coconut house.
It's this one. Has a nice deep base for lots of bedding.
https://www.amazon.co.uk/Ferplast-Al...rplast+aladino
Zooplus also do a good inexpensive one but it takes time to arrive and there's extra postage to pay.
The Savic Spelos can also make a good pet carrier although doesn't have any handles - it's a mini cage. It costs a bit more, but I found it was an excellent hospital cage for an old sick hamster, in case you ever need one.
https://www.amazon.co.uk/Savic-Spelo...s=savic+spelos