Rescued Blue tit behaviour question

Hello,

I have rescued a blue tit when it was still a fledgling around a year and a half ago in London. I got him a bird cage straight away. His feathers have been shorten as he was removing them hence removing the ability to fly too. I felt really bad at first because it is a wild bird that deserves the freedom that every bird has but bc of its condition it stands no chance outside. Right now, the blue tit has shown strange behaviour by flapping its wings uncontrollably really fast to the point where it would become so docile. When it first did that today, I found it upside down, i thought it was dead but he was just weak I think or at least very docile bc he still has a good strong grip. I took him on my shoulder and then it started to flap its wings really quickly again for the second time, as a result it fell from my shoulder (I was sat) and it just started to circle and become docile again. I am not sure what this flapping behaviour means. It’s not any type of flapping, it’s just very uncontrolled. I am saying this because it usually tweets in the mornings and whenever I go near him it starts to open its wings as in to greet me which is very cute. My family and I fell in love with helping this blue tit and we would like to do so. Obviously it is not a domestic bird but I wanna do everything possible to make sure he is safe. If anyone knows what this behaviour means and if I should be concerned please let me know. I would really appreciate that wholeheartedly. On that note, is there any way I could buy green/yellow live caterpillars for him? I heard they are very nutritious for blue tits but I don’t think he ever tried them as when I rescued him he could even fly properly. Thank you again.