I think,the question should be like this:Armstrong went to the docter with a (health) problem.
"with" can be expressed as "because of...(因为身体不舒服,Armstrong 到看医生了)".
By the way,this is a simply structural sentence:"Armstrong" works as the subject(主语) and "went" acts as the predicate verb(谓语动词); "to the doctor" is a place adverbial(地点状语),while "with" functions as "the cause adverbia原因状语l".
Such is just my view,maybe it can be helpful to you.