I know about two medications you can try, for bladder control:
Detrol, and Ditropan. Both come in generic forms (oxybutanin is the generic form of Ditropan, and what I've used for years). Both also come in a "time-release" form, meaning you take just one, and the effects are supposed to last for 24 hours.
I've found that not all of these work well for a person, and I had to experiment a bit to find what worked for me, specifically -- oxybutanin, 5 mg, one in the morning when I wake up, one at night before I go to bed. I tried Detrol, and Detrol XL (the timed release version) with little effect.
So I don't know what you were on -- but you might need to experiment a bit with another form of the same med, or a different med, or a somewhat higher or lower dose, or at different times of the day.
With the oxybutanin: I experienced a very dry mouth, nose, and vagina when I first started on it. Carried around sugar-free candies with me for a couple of weeks (or gum), to keep my mouth moist. Also found that I didn't need as much as first prescribed: the doctor had me taking it 3 times a day, and I wasn't urinating at all, causing other problems. Once I cut back on the dosage (to the 2 x day), and was on it for about 2 weeks, the very dry mouth went away, and I had relatively good bladder control. I've been on oxybutanin at this dosage for years, now...at least 10...without major incident. Very occasionally I'll have a bladder "accident" -- usually at night, usually if I am very overtired and don't wake up when my bladder "tells" me to.
Don't expect absolute control on any of these meds. You'll still have to pay a bit of attention to your bladder signals, and may wake at least once in the night, having to urinate, but generally they'll help get you back so at least you're not running to the bathroom every 20 minutes...
Other than the dry mouth upon first taking the pill, I've not noticed any other side effects. One side effect that is prominently displayed is constipation -- makes sense, as the pill affects the liquids in your digestive system, and loss of fluids is part of constipation -- so if you already have bowel problems, you should check with your doctor about dosage, and what to expect.
You should be certain, though, that your problems are the neurogenic bladder, and not a bladder infection, which can become chronic. Even with a neurogenic bladder and these meds, one can get a bladder infection!
...I am not a doctor, nor health professional, and don't pretend to be one, here.....