Eye contact is difficult when feeling vulnerable, I don't think it's unusual for people to avoid it in therapy. Crying makes us feel more vulnerable and exposed, so it's understandable to try and suppress tear, too. I think the longer you're in therapy, and the deeper the trust and bond gets between you and your T, the more comfortable you will get and the less vulnerable you will feel. I think ultimately it's a trust thing, and it takes a lot of time for some of us.
I've suffered with vertigo and nausea from anxiety, too, but I haven't had so many problems with it for a long time now. Things will get better, honestly. I think discussing this is the first step in confronting the fear and taking the power out of it.