Do post your last blood test here, with ranges. If your GP didn't give them to you, ask for them - you are entitled to them. Or your private doc may have done a panel? It is important to know where you're starting from before you start taking Erfa (although it is true that the best test of how you're doing on meds is how you're feeling). You won't want to hear this, but it is possible that you will feel worse before you feel better. Any thyroid (hormone) meds take time to work. It may be several months before you feel the full benefit. And you may find even then that you need to tweak your meds from time to time to stay in your 'sweet spot' with your meds.
What has your private doc said about how you should take the medicine he has prescribed? Clutter's advice is good, but it's odd the doc should have given you no instructions. You will need a blood test (from GP or private doc, or even a private lab) in about 6 weeks to see how things are going.
Do not be scared. For a lot of us thyroidees (particularly those who find their way here) we need to think - and step - outside the UK's restrictive medical box in order to feel well. It may be a bit trial and error - but you will get there.
Absolutely get all your vitamins and minerals in good fettle, preferably before you start - and attend to you Adrenal glands too. With all the stress your body has been under they are almost certainly exhausted. Cortisol tests are notoriously unreliable so just try a good quality supplement for your Adrenals before you start on the Erfa.