You can say "My little brother failed his history exam so he came back (or: returned) home with a sullen face." You need 'a' before 'face' because 'face' is a count noun. This applies to American English; it's possible British English uses 'sullen face' without an article. The more natural arrangement for your second sentence is this: "My coworker was sullen today because he saw his girlfriend walking on the street with someone." So,yes,you have the basic idea of 'sullen'!