If iMessage is switched on and there is no message about activation, check that your phone is set up correctly to receive iMessages: go to Settings > Messages again and check the addresses and mobile number you have listed in Send & Receive.
Troubleshoot by first turning off your mobile number or email address in the list of places where you can Send & Receive from. By trying a process of elimination we can see if iMessage works with just your mobile number or just an email address.
Also check there is a tick beside your phone number in the Start New Conversations From section
If things still aren't working you could reboot iMessage by going to Settings > Messages and turning off iMessage, then turn off your iPhone by pressing and holding the on/off switch, slide to power off, and then wait for your iPhone to start up again. Once you've rebooted, return to Settings > Messages and turn iMessages back on
Also, sign out of your Apple ID and then sign in again. You can do this from Settings > Messages then tap on Send & Receive and at the top of the page tap on your Apple ID and choose Sign Out. Then sign in again and see if this has fixed the problem.