I would start looking into nearby parishes, calling in–(and if your anxiety is too severe, try e-mailing, snail mail or fax in a written letter) and explain your anxiety, and work with the parish. You could get this contact information from parish websites, or a phone book.
The RCIA staff could perhaps work with you one-on-one or in smaller groups. Certain parishes might be better prepared to work with you than others.
I occasionally experience anxiety. I was baptized and confirmed last year and didn’t have any significant anxiety-related issues that I could recall while converting, but a few months afterward the anxiety symptoms I’d often suffered from as a teen started to return.
Attending mass became tough. I would go to the mass with the least amount of people (right away in the morning–I often couldn’t sleep, so waking up wasn’t an issue), sit toward the back of the building near a window, and wait to be one of the last queued up to take communion as to keep myself from feeling too crowded by others. Sometimes I couldn’t even bring myself to attend mass. I did seek help both within the church and with a psychologist, so I’m on the way to recovery and managing these symptoms.
Anxiety is a form of suffering. One of the best ways to cope with anxiety is to offer up those feelings of sadness, frustration, isolation and exhaustion to Jesus on the cross. Through His suffering, we are redeemed. You don’t need to make a big affair out of driving up to a chapel, saying this and that number of prayers–just stop, and pray. Ask Mary, our mother, to pray for you. Ask our saints (some of who may very well experienced anxiety in their lives) to pray for you. Ask us to pray for you. Have faith that God will help you–and if you have this faith, you certainly have the grace to go forward and be baptized.