Should I proof read it myself?

If you can show your letter to someone else to check, do so. If you are not confident about your spelling then it is imperative you get it checked by someone else. Get a dictionary and do not rely on spell-checking software as it cannot judge context. Their and there, it’s and its, should have, would have and not should of, would of are all common mistakes that some word-processing programmes may highlight for context but spell-checking software will ignore because they are correct spellings. If writing longhand, write out a draft first and then transcribe the checked and final version.