Jonah, I really do feel for you and your family. But, something isn't working here, so something needs to change.
If he is missing appointments with his therapist, not taking meds, kicking off at home, presumably not taking drugs as he's promised not to, but is going to the pub every day, and is not doing anything constructive to help himself/ his future - something has to give in order to see that this cycle is not going to continue - it's getting you all nowhere.
So, stop financing him. Now.
Does he ever have a day off the drink? Think about it - if he is not earning any money, yet is drinking daily - this will be affecting his moods and he might have come off the medication so that he can have a drink. Stop giving him money to drink and see if he has any problems going a day without alcohol - If so, get him straight to the GP, no if's or buts.
Can he take on a task or responsibility at home? Younger siblings to help with their daily homework? Take them to places/ collect them ie after school clubs - can he help you out at all and get into a more positive routine?
Could he help you with the weekly shop, help plan dinners, could you spare any time during the week to take him to job interviews or the job centre to search for work?
Try and think of anything that you could use to gradually get him into a positive routine and keep him busy (this would include looking for work) during each day and ask him to stick with it - the only way you are going to start this off though is to stop giving him money as he'll just go to the pub with it by the sound of it.
Good luck with everything