4 yo cocker clear vomit, itching, snorting

Question
We just adopted a sweet @4yo female cocker a few days ago from a shelter.  We have noticed a few things, she vomits clear/cloudy few times a day, purchased natural balance grain free bison/sweet potato and gave her this with grain free beef stew.  Hours later she vomit clear with food.  

Next issue; we gave he a bath when we brought her home using our bath wash.  She has been itching and scratching since.  She is also licking and chewing her back legs.  No paw chewing/licking yet. I started her on zyrtec 10mg this morning she is just over 20lbs.

She also snorts and snores.  All these make me thing allergies.  But my daughter wants a vet visit right away.  Any suggestions?

Answer
It takes about 2 weeks for a rescue to chill out.  Part of your problem may well be she's anxious.

Now food - she's been eating total crap at the shelter so I'd suggest feeding her multiple times a day for a short period.  Natural Balance isn't one of the best foods.  I can give you a list of premium foods if you like.

What shampoo did you use (I hope not a human one) and did you rinse REALLY well.  I suggest giving her another good rinse off.  If you left any shampoo on her it could well have this effect.  When you think you've rinsed enough, do it 10 more times.

The Zyrtec is a good idea.  Give that a week before you decide if it's helping.  

Be patient with her and allow a 2 week period before assessing any issues.