The breathing problems likely mean that you've developed (or are experiencing increased symptoms of) allergic asthma as a result of being around the cats. As the cats grow older, they throw off more dander, which may be why you didn't have that reaction when the kitties were younger. Four cats will eventually produce a LOT of dander. Did you get them spayed/neutered?
Any allergist would advise you that in order to get you properly treated, they need to start with an allergy test. But there are other shorter-acting antihistamines that could be used in lieu of Zyrtec during that week before the test, such as Benadryl or Tavist or Chlor-trimeton. Still, you would have to abstain from an antihistamine completely for at least 1 day before the test. You would have to discuss specifics with the allergist as every allergist's practice is different in this respect.
Some allergists will strictly advise you to get rid of pets to which you're allergic, some will not -- you'll have to call around and see.
There are some tactics you can use to minimize your exposure to cat dander -- e.g., keeping the cats out of your bedroom and getting a HEPA air cleaner for your living quarters and for your bedroom, getting a HEPA vacuum cleaner, washing the cats weekly to minimize dander, things like that.
And if your shortness of breath is asthma, then there are asthma meds you can use to control your symptoms -- usually a daily asthma controller along with a short-acting inhaler would be prescribed. You should know that keeping the cats will cost you in worse health (increased asthma, problems with asthma flaring after a cold or flu) and increased medication costs. Zyrtec or other allergy meds are not going to help.
You could also pursue allergy shots, which will help reduce your allergic reactions long-term, but that's a 3-5 year process before you see best results. Allergy shots will help improve allergic asthma by reducing your sensitivity to allergens. I've been on allergy shots for 6 years and my allergic asthma has improved a lot.
Hope these thoughts help. Take care & good luck.
It's never too late to be what you might have been. ~ George Eliot. A journey of a thousand miles begins with a single step.