I am writing to you to enquire about whether you would let me help out in the school's nursery for my work experience from the
Could be more formal, saying ' whether you would let me help out' sounds quite informal to me. Perhaps say something like "...enquire about the possibility of me assisting in the day to day running of the school's nursery as part of my work experience.
Also you mention you're 15 in the second paragraph - you should of perhaps mentioned this in your first oaragraph, as this ideally is where you introduce the basic info about yourself.
Also when you used the word "sporadic" just seems out of place and almost like you just used synonym checker. Generally that sentence is quite negative, you say you have sporadic exams for various subjects, don't say "various subjects, just name the subjects, saying various subjects makes it seem like your not passionate about them.
I like the whole letter though, when I was your age I didn't even bother writing a letter and did a random work experience placement that didn't benefit from at all. I think the fact that you took the initiative to write a letter and explain why your passionate about working there is great and I'm sure the nursery will see this as well.
Good Luck