I don’t think you are mentally ill, I think you are lonely and feeling somewhat trapped in your situation because of your visa issues and job stress. I think the best thing you can do right now is to focus your energy on making friends and building up a support network for you here. There is nothing wrong with wanting to date different girls and not settle down yet, as long as you are honest with them about this. Although as you have found, once a relationship ends you feel alone again, which is why you need friends too.
Try finding new and different ways of meeting people and force yourself to make eye contact and say “hello.” The only way to make friends is to put yourself in places where people are, such as the gym, coffee shops, parks, etc. You can also look for groups through things like meetup.com, take a class at a community college or find a local support group for people dealing with similar issues, including living away from your native country. If you need more help in getting connected to others you could meet with a therapist or a life coach to ask for guidance. Once you have a better support group, you may find that the job stress and visa issues are much more manageable.
All the best,
Dr. Holly Counts