-Dating apps/sites (I've heard good things about Bumble, haven't tried it myself though.)
-Date through mutual friends. Your classmates may be in relationships or super busy, but they may have single friends who are looking to date as well.
-Don't focus on dating and just try to develop genuine friendships in your class, study groups help a lot. If you find yourself compatible with someone in your friend group, a relationship may grow from that. Even if it doesn't, you'll have good friends there for you and not feel lonely.
-Try to meet students from other programs (nursing, PA, dental, PT, graduate students, masters students etc.) at your school. You can also get to know some undergrad students.
-There is time to date, don't worry. It's harder to do so, and you have to prioritize/manage your time, but it's possible. Give it some time though, I was overwhelmed and felt I had no time to do anything but study at the beginning, but you'll find yourself getting into a rhythm after a couple weeks and you'll get better at managing your study time and finding free time.
-And last but not least, try to remind yourself that being single in medical school can have it's upsides too. Like not being distracted by anyone during Step studying when you just have to focus on the test, or when applying to residencies and not having to worry about couples match or doing long-distance. Having someone there for you is really nice, but it can come with it's own set of stresses and make med school even tougher, especially if it's not a good match.
I'm sort of an introvert too, and I have anxiety issues as well, so I understand. The above is just based on my own personal experiences with dating and what I've seen among classmates. I hope some of the suggestions help.