Some addtional possibilities to your own interpretations.
Yes, a "brother" can mean a "spiritual" side, since "brother" is the word for a monk. But he can also represent something personal between you and him. A watch can indeed be the ticking of your heart, and your emotional side...but the words your brother says "Oh, now you remember it", seem to indicate that the watch is a symbol for a task you had to do on time but forgot about.
I think the "Indian" you looked up is a referral to Native Americans instead of people originating from India.
But overall I think you are well on your way in figuring out dream translation
