Someone is sending texts from my phone number. Is it even possible?

The origin of the text could be an application that has the privilege of sending SMS from the owner of the phone that it's running on and reading the phone's contacts. I suggest looking through applications on the phone in the systems menu and determining what the privileges allowed for each app is, especially newly downloaded or newly upgraded apps.

If you find an offending app with privileges that you don't want it to have, either uninstall it or revoke the privileges you don't want it to have and be more careful next time when installing outside applications on your mobile device. Always read the list of permissions that an app is requesting on installation AND when upgrading.

Someone is sending texts from my phone number - How can I stop it?

The reality is that there is no real way to protect your phone number from getting spoofed. Numbers are selected at random, so it's not like you can be specifically targeted. The only real immediate action you can take is to change your number. However, this is obviously a huge hassle and many people have so much of their life tied to that particular number. Plus it doesn't stop the telemarketer from just using your new number at some point.