Fledgling Blackbird

We have fledgling blackbirds in our garden. One spotted in the lavender bush seems fine hides and seems alert and normal. I've not spotted it since I first saw it, but I think it may have moved to a neighbouring garden through a hole in the fence. However the other seems not very well. When we first spotted it, it was raining heavily sodden and tired looking and out in the open by our swing seat. It circles rather than going straight and limps and slopes to one side. It doesn't hide and has a few sparse patches. It was however after keeping a close eye still being fed. I called a rescue who said to leave it if its being fed and hope it makes the night. We ended up keeping in a box overnight as the weather has been awful and for fear of cats and other predators and it kept falling and was looking weak and had made it's way to the backdoor. We get cats in our garden so felt cruel to leave it vulnerable. We put the fledgling back out first thing and mum was feeding within minutes thankfully. But should we take to a rescue still? As it seems lame. Or will it stand a better chance being fed by mum and out in the wild? Can they heal on their own? The rescue seemed to think it may have sustained a brain injury in fledging. Thank you from a worried animal lover.