Welcome to Android Central! Open Hangouts on your phone, swipe in from the left, and tap Settings>SMS. Does it say SMS Enabled? If so, tap it to change your default SMS app to something else. If you open any other SMS app on the phone, it will usually let you know it isn't the default, and ask you if you want to make it the default SMS app.
When you say you're texting via Hangouts on your computer, do you mean you're sending Hangouts instant messages? Hangouts IMs are not SMS (although you can merge SMS and Hangout IMs from the same contact in the Hangouts app, so that they appear in one thread). I don't think you can send SMS using Hangouts on your computer, unless maybe it's through Google Voice.
10-11-2015 04:10 PM