Samsung LG Neon

After SO long, my dearest mother gets me my first phone. I'm going on 16 in a month, but I don't really have much of a use for one other than social media. ANYWHO. It's a Samsung LG Neon. Works perfectly fine and all, but there's only one thing. Whenever I am far enough away to not receive any kind of reception, my phone switches to using internet instead. Or at least, I assume that's what that tiny little E means. Now there's a couple of concerns. I'm on a plan for unlimited texting. But instantly using the internet to text (It's exactly the same, texts just like signal texting, just with internet), will this take up any data? If it does, how much does a text take up? I have a 15mb data plan.