Hi and welcome to the forum. It sounds as if you were not given very much sensible info when you left hospital. Yes, glucose meters will store your test results, but I nearly always keep a record in a notebook as well. If the poluce ever stop you, they will be interested in the meter not the notebook, as you could write down imaginary results if you wanted.
Do you have a phone number or email address for advice when you need it ? You should have been given contact details for a Diabetic Specialist Nurse at least.