I think your ideas are clearly expressed. I'd like to point out three editing areas though:
1. If you are writing a cover letter, I'm afraid you need to use formal style, which means no "I'll" or "I've"; instead use " I will..." or "I have".
2. Leave a space in between the last two paragraphs.
3. If you don't know the name of the reader, closing with "Yours faithfully,"
- For Teachers