That is absolutely the right thing to do.
Remember to ask if endo has an interest in your health condition and if he prescribes T3 ,explain you are self paying and confirm the cost and duration of the first consultation.
If endo requires a referral explain this is difficult, as sometimes they will still see you.
Gather as much info as you can to take with you (test results, dates when conditions started, etc). I always email mine ahead so endo has time to study my notes before I arrive. You could ask the secretary if this is ok.
Be honest about your previous medical history and show you have turned a corner and want to get well.
During the consultation explain you have limited funds and ask if it is possible for your bloods to be done by your GP and any further investigative tests to be carried out on the National Health. (You will have to find a cooperative GP.) Private blood tests are expensive and will be ongoing all the time you are having private treatment.
I have had previous serious troubles on thyroid meds and wanted monitoring with my introduction to T3 and have been lucky enough to have it prescribed on the NHS (so far). However, be prepared to experience difficulties as even if you find a sympathetic endo, you will need a supportive doctor and an agreeable CCG to actually get the meds.
Just taking these positive steps is such progression.
Good luck, Flo