I'm sorry but you CANNOT, if you care about your cat, "avoid the Vet" in this case. Frequent trips to the litterbox, peeing small frequent amounts that are "pink drops" (this is blood in the urine, by the way. The bacteria in the urinary tract has inflamed the lining of the urinary tract so much so that the lining is raw and bleeding) is indicative of a URINARY TRACT INFECTION and if left untreated, not only will your dear cat continue to suffer, but she will end up with a severe and life threatening Kidney Infection.
She's in pain. She needs to see a Vet NOW - today, ASAP. There is no way around this. There is no time to sit and wait.
There is no home cure for a urinary tract infection (UTI).
There is no over-the-counter treatment for it.
As in humans, urinary tract infections are very very uncomfortable, I can tell you this from first hand experience. It is a discomfort that I wouldn't wish on my worst enemy. When you (pet or human) have a UTI, you feel tremendous burning and pressure feeling above the bladder area....you feel a constant urgency to pee and even when you do pee, it's only small amounts, and you do not feel any relief, and 10 minutes later you feel like you have to pee again (this is why your cat keeps going back to the litterbox)......and sometimes it actually really "burns" when you do pee, because the urine irritates the very inflamed lining of the urinary tract and namely the urethra (the little tube that urine passes through just before it exits the body). The pain and pressure and burning and discomfort feels unbearable, worse than a toothache. It is unrelenting until proper treatment is started (antibiotics). It is torture. I have dealt with UTIs for 25 years of my life, and I have had cats who've had them, too.
Your poor cat needs to be seen by a Vet today, there is no other alternative. The Vet will try to obtain a urine sample, and will start your kitty on proper antibiotics.
Here is a link with information about Feline Urinary Tract Infections:
http://cat-care.suite101.com/article...ract_infection
Please do not allow your dear cat to continue to suffer as she is clearly doing. She is more alert because she is in PAIN. Please - find it in your heart to get her into the Vet today. It is so cruel to allow a cat to suffer.