"My son's hand was injured but Emergency not given..."

On 22/04/2014 at 10-11pm night time when I went to airdale hospital stteeton with my little son because his hand was very serious injured due to treadmill belt by accidently .even I given him some first aid at home immediately like paracetamol and plain Vaseline for pain and moisture his hand. Triage nurse checked him very quickly, after examining he realised my son need urgent medication and reffered us very quickly to the practise nurse. But he did not check in detail and he said me , there is not need any more medication because we already have done all at home and you can go home. Even I said sir are you sure , no need any medication, not any anticeptive medicine for his hand because my son's hand's two fingers was serious damage and their skin off. There was no any option for us at last we came back home . Continuesly I was giving him normal paracetamol and plain Vaseline then second day I saw some infection in his hand then I made urgent appointment with my gp , as she saw his hand she said he needs an antibiotic. But still I feel bad if in hospital emergency they give full attention and proper first aid, might be his wound not becomes more worse.