Welcome to Android Central! Are you sure your mobile data (3G/4G) is on? Pictures can't be sent via messaging on wi-fi or voice signal--it has to be mobile data.
If you have both wi-fi and mobile data on, try turning off wi-fi. You actually shouldn't have to do this, because the phone should be smart enough to "wake up" the mobile data to send a picture message, but I've seen some posts about this kind of issue before.