With MMS, you will have a problem IF you have a VPN service running. If that is so, then you must turn it off.
just a thought, OP did not mention if VPN is in service.
I recently had trouble getting my spare Galaxy S5 to send MMS, all of the solutions were in the settings of the Textra app. In my case, all of the messages were going out as split up SMS. It was not a 'one click' solution.
forget what, but look at your message app. if the HTC/other phone SMS app is not working, then try to use another MMS like Textra which will, if set up correctly, turn ON data if it should be off.