Maybe others will feel differently about this but I don't think there's any reason to be getting letters of rec in your 3rd year (UNLESS they are for some sort of scholarship or other similar thing). When you get your LoRs for ERAS you need to have your AAMC number in the letter, which won't be assigned to you until around July of your MSIV year. If you really think you have found someone you want to write you a letter tell them that and let them know you will continue to check in with them regularly to update them on your progress in medical school. Then you send them an email every 2 months reminding them you're alive until it's actually time to get the letter.