allowed to is linked with permission.could is linked with ability
They are not exactly interchangeable but see the example below about smoking.
I wasn �t allowed to go (my Mum wouldn �t let me)
I couldn �t go because I promised to visit my grandmother that day. (unable to go because I was somewhere else)
I couldn �t go because my parents didn �t give me permission.
I wasn �t allowed to go. (lack of permission is implied)
Can I smoke in here? No. Sorry Smoking is only allowed outside. / No. But you can smoke outside.
Am I allowed to smoke in here? No, you �re not. But you are allowed to / can smoke outside.