I’m so sorry that you feel so alone. At first, I thought that you are experiencing a normal adjustment to moving so far away from family and friends. But then you said that you have never had the kind of friends you long for. That suggests a much more serious and long-term problem.
You indicated in your personal information that you are in grad school. It’s a concern to me that after a whole semester, you don’t know anyone well enough to call them and don’t have anyone’s phone number. Chances are that at least some of your classmates are as new to your new community as you are. Usually the members of a class reach out to each other. If you were seeing me for therapy, I’d be asking you to look at what you have done to initiate contact with others and how you have responded to others’ attempts to know you.
You won’t find friends or love by wishing for them. My guess is that you need to take a new look at how you are interacting with others and what you can do to invite others to be your friends. It could be that you aren’t aware of your part in your isolation. If you understood it, you would be taking steps to change it. For that reason, I suggest you make an appointment with a mental health counselor who can help you figure that out.
I hope you will follow through and make that appointment. A counselor will be a caring person in your life while you work on developing a natural support system.
I wish you well.