Welcome to the forum, justsomegirl
I have to say - I wouldn't feel very comfortable if I had a Vet who couldn't see one of my cats within a day/two for an acute but non-urgent issue. Perhaps you haven't fully explained the delay - but, if it's strictly because of 'busy-ness' at this clinic, I'd urge you to find another Vet.
Now, you sound very confident about that - well, do you think it might be a sterile abscess
? Make sure you read the 5th and 9th reply in there.
Just on the Vet issue again - I would want to have a competent feline Veterinarian. They can usually be found at cat-only clinics. Sometimes they are members of The American Association of Feline Practitioners who have a Vet-finder page here: http://www.catvets.com/cfpandpractitionersearch/
Now, "simple" membership doesn't ensure competency - but, it does make for a surer starting point.
Hope some of that helps.
Keep us posted!