Might be a plan. I have the similar kind of problem and had the CBT appt like you and then have not taken them up on it.
It was supposed to be something called intensive CBT one hr a week for six weeks and I just got bad vibes about it.
I don't think I'm really having thoughts that are out of proportion to what I am facing to be honest and not sure it would work- and I have a CBT book so know what it is about.
the truth is it is not an easy situation and requires a lot of adjustment and I don't want them minimising it etc and not understanding,. It can be frustrating talking about health conditions they don't understand.
I think it would be better if the ME clinic did more counselling really as they were quite good. I liked the way they said they are 'prescribing rest' for us and talked about restorative activities which were easy and not stressful and talked about the grief cycle as well.
I'm starting the realise that all this dealing with other people who don't get it is also taking up a lot of energy but I don't want to lose them from my life as well.
It's a difficult situation to be in, and I don't think people get it really unless they have been there.