I think you need to talk to your doctor about the medication. I looked on Drugcite and while I didn't see anything directly stating memory problems, the #1 group of SEs are neurological. I did see speech disorders as #8 most common and I'd bet at least some of your other symptoms are there if you want to look up all the '..eugias', '..agias', etc. Click to expand list. I 'm not familiar with your disorder but read that it is due to hyperexcitability. Think about it this, if Tegretol calms that it could also be depressing your cognition and performance as well, its all related.
I saw a forum for the disorder but can't do links right now. You might want to look for it and see what meds people are taking, I looked briefly and did not see tegretol. Have you always been on it or was it prescribed after others were not effective?
I'm not a doctor and I could be wrong but I've had some cognitive issues with medication as well and I think its possible that is what is happening. Please talk with doc and try to find more information.