Hi JulietAnne,
Are your email messages from a POP or iMAP account? Your profile indicates you are using iOS 6.0.1. If possible, I would suggest backing up your iPhone and updating the iOS to the most recent version which is 9.2 to address this issue.
Back up your iPhone
https://www.apple.com/support/iphone/backup/
Update the iOS software on your iPhone, iPad, or iPod touch
https://support.apple.com/en-us/HT204204
Take care,