CBT is such a common therapy method that almost every therapist is trained in it. Within the CBT "family" there are many different ways to structure the treatment. It will all depend on your therapist, how much they know about emetophobia, and what their beliefs are about exposure therapy. I would ask about all of the above. Your first appointment will normally be a "get to know you" session, or as we call it in the biz "intake" or "presentation." After that, it varies a lot. But remember that you are in the driver's seat. It's your treatment, your hour, your money. So you're in charge. Don't ever agree to something you don't want to do.

As for only being afraid of others, that's the easiest form of emetophobia to treat. I suffered from that as well, in later years particularly. Your therapist will probably want you to make a "hierarchy of fears" - a list of what you fear least, all the way up to worst. Then they start with the least feared thing and work on desensitizing you to it. That's the "behavior" or "B" part of CBT. Some CBT therapists are more about the "C" which is "cognitive." They want to change your thought patterns, or the way you think about the phobia. Some people on here have experienced frustration with CBT when it gets geared too much to thoughts and they're not "doing" anything. So again, you're in the driver's seat!

Good luck!