Managing personal Outlook.com account settings, security, and privacy
No, reading phishing emails won't make your account compromised. Just makes sure you don't click any link on that phishing email.
Having said that, The following article below will help you secure your account:
https://support.microsoft.com/en-us/account-bil...
If you need to bring your account security protection to the next level. In the following article, I explained how to do so: https://answers.microsoft.com/en-us/msteams/for...
Kind Regards