Android Messages can't send images
You might be having a number of APNs pre-loaded on your handset. Just keep the right APN and delete the extras. Keeping only the right APN will force the messenger to use that particular APN.

Follow this path for deleting APN.

Settings &rarr; Wireless and Network  &rarr; More   &rarr; Mobile Network &rarr; Access point names.

To find out which APN to keep refer this documentation.

PS. After deleting APN, if you face network issues, you can simply reset it to default by  Settings &rarr; Wireless and Network &rarr; More &rarr; Mobile Network &rarr; Access point names &rarr; menu &rarr; Reset to default.

Hope this helps.