Baby Chaffinch?


my children came home with this little one a few days ago after finding it next to a dead parent and siblings. I took it back to where they had found it and put in the nearest bush amongst the undergrowth for the other parent to find. 

I went back to check the next day and it was in the same spot I had left it. Still chirping very quietly I stayed to see if the other parent came to feed it. Nothing Came for an hour so I decided to leave and go back the next day to check on it. I went back the next afternoon but couldn’t hear it chirping so assumed the other parent had been to feed it. I checked the spot I had left it and it was still there but cold and not vocal at all. It was obvious that the other parent hadn’t come back to feed the little one.
I couldn’t leave it there to die so decided to bring it home. I made a little nest and put a hot water bottle underneath the box to give warmth. After a few hours it started to make little sounds. I mixed a little cat mousse with cooled boiled water to see if it was hungry. It ate a little then I put it back into the nest I had made. 

I am in day 3 now and have an egg food that I moisten and feed every few hours. It has really perked up and is very vocal which is lovely to see. 

I am now concerned that it may of actually been injured in the attack in its family as it’s left leg doesn’t seem quite right. It has started perching one my finger yesterday but seems very lop sided. 

Would anyone be able to tell me what type of bird this is? 

Also if I should take it to the vets now? I rang a local wildlife lady when I found it originally and then when I found it again lifeless. She advised to leave it there and wouldn’t take it in. I don’t want to contact her again. 

I’m happy to continue to look after it, hoping it would be strong enough to go into the wild in a week or so once it’s strength is up and flying. 

Just if it is injured I’m sad that may not be the case now. Please advise.