I am a 22 year old male and often develop severe anxiety when faced with certain public situations, like eating with strangers or speaking in public. Is there anything that can relieve my anxiety?

You most likely have social phobia, which is a very common disorder. Often people with this disorder develop anxiety in public situations. Like almost all disorders in mental health, there is always some bogus psychotherapy. I am not sure how talking for hours on end can help relieve a mental health disorder. In addition, psychotherapy is not cheap. Much of it is plain bullshit common sense.

I would recommend you see a psychiatrist and try out a medication. There are some very effective medications like the newer antidepressants that work. However, all medications have adverse effects (and are also expensive), so it is important not to take them for too long. Most mild cases of social phobia can be treated and have a good prognosis.