It is doubly confusing as the message symbol normally indicates going to a message/inbox. Whereas symbol for sending tends to use a stylized arrow.
I’d say, change the button to Send with a ‘mail arrow’ icon.
Also this:
Looks like you’ve received a new message and need to click on the button to view. If you want to write a new one, then better to have a ‘pen’ icon and ‘Compose’ language.