Speech impediment and making friends?

[quackly duckling]

At some point in my life, I developed a speech problem that makes me stutter and stammer. This continued all through out high school which played a key role in presenting me a major challenge in making friends.

Now in college, the problem persists, and I have zero friends mainly because of my speech problems. People come and talk to me generally, but when I talk back to them, they look at me funny and then eventually keep their distance away from me.

I have no social confidence at all, and I had less than 5 friends in my entire life. As you know, humans are naturally social creatures that require them to verbally interact with one another in order to carry out what you call normal every day lives. I can't go see a speech therapist because I'm just a student, and financial status is definitely an issue for me.

How can I make more friends or at least maintain my relationship with other friends?