I don't see why I have to have a GSM shield if the board it self is not communicating through the cell service rather generating the commands to send a predetermined text, kind of like those pre-configured quick replies.
The board? Which board? Are you referring to the Arduino? How is it "sending the commands"? To what?
By all means, go ahead and try to send text messages without a GMS shield. Let us know how you manage.
Do AT commands differ between phone manufactures? I saw somewhere they are pretty similar.
Similar != identical.
Would creating an android app be the easiest way for this?
For an iPhone? I doubt it. If you have an Android, and the skills/capabilities to create an app, and the hardware to communicate with the phone, and you want to dedicate the phone to this purpose, by all means, go right ahead.