Students keep crying in my office

Title says it all. I am a non-US faculty in a college in the US. I am also one of the few international faculty members here. Many international students come to my office hours, talk about their lives, and end up crying. They talk about their stress, anxiety, and loneliness. They miss their home and family. They tell me they are worried about what will happen to them after they graduate, after they lose their student visa status. One student had a panic attack in my office while talking (I had to carry the student to EMS).

I feel terrible for these students. They have no one to talk to except for me. And all I can tell them is to seek counseling services and other campus resources. At the same time this is really affecting me negatively. I guess I am lost — how do I be an empathetic human being without carrying the emotional burden?