Ugh. I feel for you. Kidney pain like that is just shocking.
My daughter has suffered with recurrent UTIs for some years although her problems have been due to anatomical abnormalities mostly. She's only got one kidney and ureter now but has a mega-ureter so urine pools in that area and often will reflux back up into the kidney. She also doesn't really feel the urge to urinate which causes more problems. During one episode she ended up with septicemia. That was when she had both kidneys. They ended up stenting one kidney but it didn't take. Long story...
She has her own testing strips now but still that means that if she's got some sort of infection they feed her antibiotics which is not ideal but otherwise it's difficult to treat and because she's only got the one kidney she needs to keep it.
You could try Cranberry juice in your daily diet or the tablets which you can get at the Health Food Store. Probably supermarkets as well these days.
There's also the urine neutralizer which she's been given from time to time. Ural. That just tends to stop burning and it's a good idea to talk with doctor before using that.
I'm surprised they've sent you home while you still have that pain. Sounds as if you've still got an infection. Drink LOTS of water and when you do pee, make sure you really empty your bladder. Might be difficult while you have this frequency feeling.
It's a real worry to be home on the weekend still feeling so sick. If that pain persists I'd be going back to the hospital or doctor asap!
Do you have a fever still???
Should I see a urologist?