起きる and 起こす: waking up and events happening
Distinguish the person waking up from the person doing the waking, then compare the verbs when an accident occurs.
Getting up after an alarm
明日は六時に起きます。 means that the speaker will get up at six tomorrow. 起きる, read おきる, has the person getting up as its subject and uses に for the time.
起きてから顔を洗いました。 says that someone washed their face after getting up. 起きて is the te-form of 起きる; getting up comes before washing.
Wake someone else
七時になったら、私を起こしてください。 asks someone to wake the speaker at seven. With 起こす, read おこす, 私を identifies the person to wake.
赤ちゃんを起こさないように、小さな声で話しました。 says that someone spoke quietly to avoid waking the baby. 起こさない negates the action that they are trying to avoid.
Events unrelated to sleep
交差点で事故が起きました。 reports an accident at an intersection. 起きる refers to occurrence, not waking up, and で marks where it happened.
事故を起こしてしまいました。 says that someone caused an accident. 起こす presents the event from the causing side but does not establish intent.
Who is to wake up in 私を起こしてください?
Show the answer and why
The speaker, 私. The person addressed does the waking, and 私を marks the person affected.