Hi, Sheila,
This really a case for a vet to sort out. You do not say if there is increased frequency - for instance, can she go all night?
The cause could be cystitis ( inflammation/infection of the bladder wall), or a growth anywhere in the urinary tract from the vulva to the kidneys.
I always dread to hear someone say they do not want ' to take her to the vet in case she has to be put to sleep' . The number of times I have heard that, and had to reply 'If you had brought your pet to see me three months ago, I could have saved it, now it is too far gone to treat'.
Maybe try a different veterinary practice - she will remember the one where she had a bad experience. May be go in and talk to the vet before you take her, to make an appointment and maybe ask if they could give you a mild tranquilliser for her.
I hope all goes well for her./
Walter