Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Everyone who possesses the amount of money that reaches the Nisaab has to give its Zakah right after completing of a lunar year. He has to give the Zakah of his money in the same country where he has his money. If there are no needy people in that country, he may transfer it to another country where Muslims are poor and need money. It is forbidden to delay giving Zakah if one is capable to pay it in its time.
Therefore, dear brother, you have to give the Zakah of your money if you are able to carry it by yourself by traveling to your country; otherwise, you have to deputize someone who gives Zakah on behalf of you.
Know that providing free of charge services to patients cannot be an excuse for you to neglect this obligation. Zakah means giving a certain amount to the deserving people and putting it in their ownership. Finally, we warn you against being careless in performing this obligation, i.e. paying Zakah since it is a pillar of Islam.
Allah knows best.