Your lettering is very dense so you need to really stabilize your fabric. What stabilizer did you use, and how many layers? Also, when you hooped your fabric you may have stretched it a bit.
I rarely hoop fabric anymore. You can hoop the stabilizer, place your fabric on top, and then use the baste in the hoop function to tack it down onto the stabilizer. (Not all emb. machines have this function)
OR
You can hoop the stabilizer, and then spray the back of your fabric with Sulky KK2000 Adhesive Spray (great product you can find at JoAnn's-use a coupon) and then lay it on top of the stabilizer.
This is why every book on machine embroidery cautions embroiderers to test out new designs on the same or similar fabric. Better to use a little extra stabilizer and thread than to ruin your garment.