Most schools provide a letter storage service via their career center or similar resource. There are also online letter-holding services such as Interfolio.
You can ask your letter writers to send the letter directly to the service or upload it yourself whenever they are ready. The letters must be signed and should have an official letterhead. Acceptable letters are then the letters uploaded into the service.
You will be able to use these letters later on when you are applying to medical school. These services are secure. They will not allow you to read the letter beforehand.
You can upload letters anytime and feel confident that they are safely stored. This is particularly helpful because then you can use the letters when you need them.
Using a service like this prevents last-minute scrambling when it is time to turn in the letters for your application.
