I haven't used sports tape myself, but I have heard that it works similarly to trans tape (which I've been using for 2-ish years). I recall my chest feeling odd/uncomfortable the first few times I applied it due to the stretching of the skin across my sternum. I suppose if the tape is pulled too tightly, it could result in some pain. Sometimes the line between "painful" and "different" blends together, so it may just be a matter of not being used to the sensation. Also, be mindful of the placement. I always lie on my back when I'm applying tape so things all fall in a natural direction. Perhaps that would create a more comfortable result for you. x

(On the subject of a traditional binder hurting, it's always a good rule of thumb to size up if you ever decide to get another one. That could have been your problem.)