Hi and welcome. I first need to say that we are not medically trained, are not experts and are not mental health professionals. We are, however, a community that understands the impact mental health issues put on those of us who suffer, and our friends and family. We offer support and friendship to anyone dealing with this in their life.
That said, it’s great that you want to help your brother. Encouraging him to take the medication and therapist are both things you absolutely should be doing. With the medication, it normally takes 6 - 8 weeks for anti depressants to get properly in the system and seeing an improvement in mood so 20 days is not enough time for him to feel better. Perhaps understanding this would help him to try again?