I can relate to your experience a bit minus the fact that I don't have social anxiety. I'm also in second year and have no friends, not even one. I have tried societies and gained nothing but acquaintances who eventually turn into strangers. I'm going to try a few more societies and speak directly to the student union saying I'm struggling to make friends and so and hopefully they can direct me to some of the fun, interesting and sociable events people are likely to be at. I have hope and don't want to get to third year with no soul.
I think you have good ideas, you should pursue them. talk to your class mates and join a society.