She might just be settling in and it's a phase that will pass. There's a difference between new dogs nervous about being left alone and dogs who truly have separation anxiety. So I wouldn't look to medicate or anything right now.
The suggestion above about "leaving" and coming right back is a good one. Doing sessions like that every day will get her used to people leaving. Don't just keep increasing the amount of time, either, occasionally come right back in, etc.
This is a rather expensive suggestion (unless you get lucky on craigslist or something) but a large outdoor dog kennel would keep her contained. There's no way she could chew out of that! If you know of someone with an old one they aren't using, they might give it to you.
I agree with not locking her in the crate right now. If she's that anxious, she might injure herself. I fostered a spaniel/retriever mix with HORRIBLE SA (much worse than this situation) and he would manage to break through the crate, urinate all over himself, crash into things, etc.
At this stage she's probably just feeling anxious because she doesn't know if you're going to come back. It's a common phase for rescue dogs (and even new puppies) and many grow out of it
. Just hang in there and give her lots to do when you're gone--Kongs, bones (only ones she can't break pieces off of unless you're around), puzzle toys like the Tug-a-Jug, etc. Make sure she's getting plenty of exercise (a quick walk around the block or some outside playtime isn't enough for most dogs--you want her to really move and be exhausted).
I had suggested in another thread to give her meals in her crate and I'd definitely still recommend that
. That will help her warm up to the crate faster.