Yes, you can train your dog to remind you to take your medicine or any other consistent task you need to do every day as long as this is something you can have the dog remind you to do at the same time every day.   

Your dog has an internal clock, so you are going to teach him to tell time.  

Be careful with this one though, because if you’re only on the medication for a short period of time, you will still be reminded at the same time every day. 

With this task, feed your dog at the same time every day.  Try and make it as exact as possible. 

As soon as you have a routine established, you are going to delay until your dog offers a behavior to remind you to feed him.  This could be a bark or a nudge.  Praise him and feed him immediately. 

If you get no response, make the bowl of food, put it out of reach and walk away.  If there is still no response continue to feed at the same time every day.  You’ll need to give your dog more time to catch on to time management.