Sudden vomiting and refusal to eat.

My cat is 12 years old and has been healthy her whole life. She stopped eating Friday and has been extremely lethargic (which is very unusual for her) as well as vomiting. The vomit is a frothy color. I took her to the vet Sunday and he did not seemed too concerned, however I feel I did not express how sick she has been acting. We are going back to the vet tomorrow, but I was wondering if this has happened to anyone else. I am so worried about her! 

You really need to get some food in her.  Going without food for any length of time can lead to other health concerns.  Get some canned food and a syringe and syringe feed her.  Add some water so she's getting some water in her, too.  When you take her back to the vet, have him do a senior blood panel to check her kidney values.  It's possible that something's going on with her kidneys and/or she may have a urinary tract infection.
 

He gave us anti-anxiety meds thinking it was behavioral, but they have yet to help. The syringe is a good idea! Thank you! 

I find it strange that the vet thought it was behavioral and gave you anti-anxiety meds. Vomiting and lethargy seem much more likely to be caused by a medical reason. Were any tests run? I definitely second running full bloodwork and a urinalysis.

I also definitely agree with syringe feeding. Cats cannot go long (24-48 hours) without eating as they will be at risk of developing fatty liver disease.