気分: a refreshed mood or feeling physically unwell
Compare feeling refreshed after a walk with resting after feeling unwell, using the surrounding action to identify the sense of 気分.
Feeling refreshed after a walk
気分 (きぶん) can refer to mood or physical condition. “朝の散歩をすると気分がすっきりする。” says that a morning walk makes the speaker feel refreshed.
Read すっきりする together with the walk: this example focuses on a refreshed feeling. It does not establish that a particular physical symptom has disappeared.
Resting after feeling unwell
In “彼は気分が悪くなり、静かな部屋で休んだ。”, he felt unwell and rested in a quiet room. Read 気分 here in line with that physical-condition translation.
休んだ states that he rested after feeling unwell. The sentence does not specify a disease, the cause of the discomfort, or whether he recovered after resting.
Use the surrounding action to identify the sense
Compare すっきりする in the first example with 悪くなり、休んだ in the second. The same word points here to a refreshed mood and an uncomfortable physical condition.
Do not always translate 気分が悪い as feeling offended or angry. Conversely, do not make every use of 気分 refer exclusively to physical condition.
Can the quiet-room example be read only as resting because he felt offended?
Show the answer and why
No. The supplied translation and the resting context describe him feeling physically unwell. The sentence does not state an offended feeling or a specific disease.