Doesn’t make sense to me: you were either so ill that you needed to see the GP the second time and a wishy washy answer without examining would clearly have caused you to question it at the time, or you were happy enough with the answer at the time because “you felt better but not perfect”.
Now if you genuinely believe that the doctor is a “danger” then fair enough make a complaint – but if its just for the sake of kicking up a fuss then probably accept that everyone can’t be brilliant 100% of the time, and that the practice will be keen to show (publicly at least) that they have not done anything wrong. If I was making a complaint here – rather than putting it on paper (which WILL get a formal but not necessarily effective response) I would suggest calling the practice manager and asking to meet them and one of the partners to discuss your concerns with the aim of avoiding making a formal complaint. IMHO that is very likely to get more attention that a letter which will probably produce something along the lines of “Thank you for your complaint. We have conducted a thorough internal investigation. Unfortunately the Dr who treated you does not recall the same details as you, and recorded in your patient notes at the time that you were feeling better. It is not uncommon for patients to show signs of improvement before the recurrence of an infection. Our investigation has therefore not identified any error. We have however reminded the doctor involved that it would be best practice to examine the tonsils of patients recently presenting with tonsillitis. You have a right of appeal, bla bla.”
Oh, and if you’ve only had 1 day in bed then I’d argue that’s not “proper” tonsillitis!