The consequences of missing credit card payments

I have four credit cards; ADCB-2, HSBC-1 and FGB-1 and loan. ADCB credit card and loan I'm paying without any delay, but HSBC & FGB I paid last month after collection dept calls.

My question is, next month I'm going on vacation. So will someone stop me at the airport immigration?

Again, I want to say that. The beginning of this month, I applied for a top-up loan to close all my credit card outstanding.

Today I received a call from ADCB that my application is declined. They are asking for a report from Etihad Credit Bureau.

Does it mean they will file a case against me?

Please, I need your advice.