I too have asthma and also live in the UK. I personally have been given excellent treatment for my asthma problems at the general surgery I attend. I am with the others on this, I just don't understand why you have not been given a nebuliser on prescription for home use. You say that you go to the children's hospital. Does this mean you are under 16 years old? Surely at this age you are entitled to free prescriptions.
Something is drastically wrong if you have to go out to the hospital every time you are ill. Can you not call the doctor out? He can then see for himself how bad you are, and then your parents can ask him for a nebuliser for use at home for you.
I hope you can sort something out.