I would call a different vet and get a second opinion if possible. Some just don't want to treat cats for snakebite. I have seen many cats, kittens, dogs and even a horse die from snake bite here. This year was particularly bad for rattlesnakes. It can be up to 48 hours before they die even in a small cat.
The benedryl is to slow down the allergic reaction and swelling. If her head is swelling that badly she may need a stronger anti-inflammatory and also pain killers....not metacam, but buprenorphine. Keeping her comfortable and pain free is going to reduce the shock response. Fluids is another thing that may be necessary.
Anti-venom is really expensive $300-600 and it sometimes does nothing or actually makes things worse. It doesn't have a long shelf life and vets don't like to keep it on hand. 4 weeks ago my vet said he couldn't even get any because it was on backorder.
All that being said she is little and odds of survival are not great. Dogs now have a rattlesnake vaccine that works very well at reducing the reactions to snakebite, but even some of them die.
I am sorry to have to be so honest, but I don't want you to have false hope. It is most definitely not certain your kitty will die, with lots and lots of supportive care ( the more you can learn to do at home, like sub-Q fluids and giving shots the less expensive it will be) she can certainly survive. It is just that the odds are stacked heavily against her.
I am sending lots and lots of recovery vibes for your little girl
You need to carefully search around your yard for that snake. It is getting colder and they are looking for places to curl up for the winter.