I think it's great you had the courage to post here, it takes a lot and I'm sure comes at the price of more worry. It's a pretty good thing to do though, as many here will have had similar experiences.
For some people social interaction is just a little difficult, and those people are called shy. There are different degrees of difficulty however and greater shyness can be a symptom of an anxiety condition. I've had chronic anxiety, plus some other things, for a very long time and can have problems in social situations too when things are bad.
You said that it is not only uncomfortable for you, but very worrying as your job, and relationships with others plus studies can be affected.
At this stage I'd suggest, if it was me, that I'd see my GP and ask to be tested for anxiety. You can write - ok write down in detail what you feel, what is happening to you, and how long it has been going on. Share that paper in a long consultation -that's how I find I can get everything out properly.
Then see what your GP and the tests show. If warranted you may end up on a Health Plan with visits to a psychologist and therapy, as well as guided self-help. The good news is that anxiety is treatable and normally responds well.
I'd suggest you look up anxiety; causes, types, symptoms and treatments in The Facts menu above, also have a look at how others have coped in the Anxiety section of this Forum.
I'm sure that things can improve for you. I personally am in a much better place than I was.
It's funny you mention writing, as I tend to write out old happy memories as a means of coping when I'm not too good - such as reliving a conversation; similar to what you mention.
If your doctor agrees you can go to the welfare/mental health section of your uni and register, then you may have help if you cannot meet deadlines, and with academic penalties. They are bound to keep your details confidential.
Please write again as often as you'd like