1. Try Schmetz 90/14 or 80/12 Quilting needles or Universal needles. There's a good chance your needles are poorly machined in the eye and have sharp edges that are shredding the thread.
2. Is your cotton quilting thread old, dry rotted, or an off-brand? Try one of the classic thread brands mentioned on this board (do a topic search), such as Mettler, YLI, Superior, Connecting Threads Essentials, Sulky, Aurifil, or so forth. Store thread out of direct light or dust to preserve it.
Jan in VA