Short answer
An engagement is a promise or agreement to marry in the future; it does not itself make the two people husband and wife.
Islamic Guidance
What Islam teaches
The legal marital relationship begins with a valid Nikah, not merely with an engagement or family announcement.
Practical Guidance
What you can consider
Keep the distinction between engagement and Nikah clear and continue observing appropriate boundaries until marriage.
Sources
Qur'an 2:235; Sahih al-Bukhari.