Help! Triangles Sticking Out of Mesh

Hey! First thing, do not make your mesh double sided if it is not needed (it's used for meshes with transparency mainly), it's not how clothes should be made for sims. Instead close holes at cleavage, bottom and sleeves and edge split them to keep sharp shading. It not only repair your problem (your inside part is the spikes you saw, they moved weird while using sliders, I think it could be that you probably used 0 thickness while making it double sided) but greatly lower polycount of your top (from 11,4 to 6,8). Now as you deleted body parts, made your mesh double sided only and then you'll look from the bottom or top you'll see that there is nothing under top, no body just hole.

Do not transfer weights and uv_1 to body parts, join them at the end when everything with your top is ready. As a reference use top with cleavage covered, you'll get better uv between breasts - now it's stretched. After tranfering weights use Clean (All Groups) and Limit total (limit to 4).