What is the ruling of Islamic law on paying money to officials in order to facilitate travel procedures, knowing that this is the only way to travel given the lack of job opportunities in the country?

It is permissible for a Muslim to spend money to obtain a medical examination that he cannot obtain otherwise, in order to be able to travel and seek livelihood. There is no sin upon him in doing so, as it involves repelling injustice from himself and attaining his right. The sin falls upon whoever takes money unlawfully.