Sounds like an infection yeah, though my bladder does tend to want to empty itself when I can't normally as well, as gets worse before I go on road trips etc.
But it sounds to me like its not phycological, unless your brain is physically sending urine to your bladder because of a signal its sending out, and far too quickly.
Or are you going when you get home, even though you are feeling like you are full, and only going a small amount? If you are, I would certainly think an infection.
I'd still go to the doctors again like people have been saying, and explain it.
It's not too late!