That's not so bad then. I think it is maybe a bit difficult for GPs to interfere with what an endo has prescribed. Pity he wouldn't test your blood more frequently while you are getting sorted out. What are your other results like - do you have TSH and T3 done too? Have you ever had B12, vitaminD, ferritn and folates done? You'll feel better if they are all well up within their ranges.
I know first time I needed an increase my GP wasn't keen to do it hence the amitryptiline - can't take beta blockers or I would have been given them. Next time she gave me a little increase to take every other day - well it was meant to be taken Monday, Wednesday and Friday but I went for every other day.
I'm not surprised you feel terrible going up and didn't like that. When I was under and was SO cold. It was mid summer, warm and sunny and there I was wearing denims, a vest, t shirt, jumper, my winter quilted coat, scarf and gloves and still feel cold - at one point I was sitting amount people in the waiting room who wear wearing short sleeved t shirts. I stripped it all off to have bloods taken and no one seemed to think it was the least bit odd! I was even taking a hot water bottle to bed every night and had a blanket over the duvet. Once I had my levo increased and became less hypo which I suppose for you would be like having your carb reduced I went back to normal - that easily.
Apart from wanting to hang onto my thyroid for as long as I can - even if they kill it off I will still have Graves - I just won't have a thyroid for it to attack - I don't want to have RAI because I think it is the easy, quick way for the hospital to get rid of you - once you are hypo they can pack you off out to be dealt with by your own GP. Or that's what it feels like to me.
You were at a level where you felt good were you not? When I needed my levo increased used to say to my doc / endo 'I have felt good in the past and I know if I have a raise in my levo I will feel good again' and that usually worked. Try telling them that you have felt good in the past and once you get on the right dose you will feel good again. I kept a record of all my test results so that I knew where I had to be within the range to feel could. Could you do that?
Hopefully someone who is being or has been treated by titrated with Carbimazole will come along and tell you how they are managing - there are people doing that on here.
Put Carbimazole into the search box at the top of the page and see what comes up - you might find some helpful posts.