Im korean so im not good at english nut i want to explain to you.
'미국이랑 한국에 들러요'
This is correct sentence.
'들려요' is '들르+어+요'
Base verb is 들르다
들르다 means go somewere.
들리다 means something is heard(this is the passive word), holding by somthing, rasing by something, cutted because its rased, etc.
Acconting of 어 is very hard for begginer so you can study about that.