Hello,
Yes, I oten get sick due to anxiety. It is more common for me when I am feeling additionally depressed or the panic attack is quite sudden and tunnel vision throws my balance way off. It's not consistent for me but if it happens every morning, maybe that is when you feel the most stress. I think throwing up can be a physical release to a mental stresser or an imbalance in equilibrium (tunnel vision dizziness) so, in my unprofessional opinion, it makes sense that you would get sick at home. You feel safe there, and can eliminate some of the stress in a physical way instead of bottleing it up like we have to do at work or in public. Just a thought. Hang in there!