Hi, Rosemary15. Welcome to the site, though I wish you'd found us under better circumstances...
Our Priscilla would also have sneezing fits. Occasionally she would sneeze out a blood clot, but then the bleeding would begin again. Did Rosemary have increased bleeding after she sneezed out the piece that you brought to the vet?
I hope the vet can find something out from the tissue you brought in. The rhinoscopy can be expensive (as you're finding out) and often is inconclusive as to whether there's a mass there. The rhinoscope can only go in so far so it can't detect tumors that are way back in the nasal passages. If what Rosemary sneezed out was a piece of tumor, or part of an abscess, the vet may be able to determine what the problem is without having to use a rhinoscope. Did he send it in to a path lab?
We had a rhinoscopy done on Priscilla and they did a flush at the same time. Occasionally, especially in dogs that use their noses a lot, something like a grass awn or some other irritant will get lodged up in the passages somewhere and cause bleeding. A flush will sometimes dislodge such material. Since we didn't know what Priscilla's problem was at the time, we were hoping it was something lodged in her nose. The rhinoscopy was inconclusive and the flush was unsuccessful. Unfortunately, in the end, it turned out she did
have a tumor, although other than the vague x-ray suggestion of a mass well back in 'snout' of the skull we never really did know where it was.
With Priscilla, once we had convinced our hearts that she had a tumor, we concentrated on keeping her happy and comfortable. Surgery was not an option for her, either, since she was also 15 and we weren't even sure where the tumor was.
My heart aches for you, because I know how you feel watching your girl and worrying. Wish I had better advice for you.
Just know, that whatever you decide to do or not to do, it will be the right choice. This is a hard situation to be in, with no perfect answers, but if you make your decisions with Rosemary's best interest in mind and love for her in your heart, you can't go wrong. Please keep us updated.