Your cover letter seems adequate to me. There are some gramatical errors which need attention and this should be addressed before you send the letter – Microsoft Word or similar will highlight the errors.
Your letter clearly demonstrates that you are keen to learn and motivated about working in the vacancy. I would certainly include details of your previous experience as although it may not be directly related there are relevant skills – dealing in the medical profession, working with people, time management, paperwork etc. You should be able to review the job description and pick out items which you are already familiar with.
We wish you the best of luck and would like to hear how you get on.