My Catheter removal experience was similar to yours. If like me you had just drunk lots of water for your TWOC it is also quite understandable. When I post about Catheter removal I usually advise a towel for the journey home.
I experimented in the shower with pads and found like you a sudden gush would not be contained by the pad I was using but contracting those pelvic floor muscles would slow things down enough to allow the pad to absorb the urine successfully.
Standing and getting in and out of a car are frequently mentioned as hot spots for leaking, using the pelvic floor muscles before getting up in the key and standing up slowly might help.
Are you doing the exercises already , is the physio appointment for additional help ?
If you can stop the flow mid stream that is a good sign, but doing it all the time is not good for the bladder.
You will have heard it already but early days yet.Hopefully in a few weeks time, there will be a marked improvement.