For me, bladder issues like the ones you describe started when I started mestinon. I never had any bladder problems before using mestinon, even though I had weakness for a year before diagnoses.

If someone stays with me for a day, they're all like because I pee waterfalls every hour or so. They're like; how, why, what, where does it come from!
In the car when it's over an hour driving, I always have to say: can you stop? Drivers always say kind of grumpy: can't you just hold it for 15 more minutes or so? ehh...NO! Because like you, when I need to pee I really need to find a toilet in 5 minutes.

I'm loosing pee too sometimes, which sucks.
Luckily, I do not experience any poo losing problems (I am almost fulltime constipated so am already years more in control of poo because I use medicine to go and they work in 2 hours so I'll just plan my poops... Yeah okay, maybe tmi )

Anyway, be sure to have it checked.