The vet can't possibly know whether or not she should be seen by a phone call because something may not be being described to him/her. I would wonder why they don't want to see her and if you end up taking her and there is a problem, I would be very upset that they didn't insist on seeing her after your first call.
After Ellie's spay I didn't like how her incision looked twice and both times they saw her for free the same day or the day after.
As for the throwing up with it, I'd go to the vet as soon as possible.
Welcome to YT
