My 10 months old chihuahua is sick. He threw up last night and early this morning right after his walk.?

His vomit was just really white and hy. I think he might have eaten something during his walks. I read somewehre that you should not feed him for about 24 hrs, and let nature take it's course. But tjhen it could also be that the resident dog (7yr old chi) punked him so bad while I was gone last night that he's just really too fearful now. I just got the 10 months old about 3 weeks ago, and yesterday was the first time I left him for more then 2 hours. What could it be? Physical or Mental? Sorry My story was too long. But any opinions will be greatly appreciated.