Sux...with pets being sick more than a couple days should be a trip to the vet. With cats some things can kill them in 24 hours (like urinary blockages).
Also I'd find another vet...for them to tell you 3-6 months without even xrays or exploratory surgery is a guess at best.
Most think their vets are the best. The vet I use and interned with while in Zoology has probably saved 20+ pets whose original vets said were terminal.
Sadly most vets (people doctors are not immune to this) don't stay on top of their game. They get the routine shots, declaw, sterilization, broken limbs, colds and eye/skin issues.
The dog I just got when my grandmother passed away has cancer. She's not showing any signs. Even after removing her spleen she's unphased. There is a huge tumor in her lung though which means the cancer spread.
Going in to remove it is about 4 months of recovery (she's 12 and in her normal lifespan range already)...then we risk another tumor showing at that time. It's the left lung, which the right can take over for....but she's dealing with having only 2-4 years of life left if healthy.
We are going back for xrays in a month to see if the tumor is growing and get some more information for radiology interpretation...stinks when pets get sick.