Are there any potential complications you could have from tearing off a toe nail?

Maybe. After having a nail (finger or toe) removed or torn off, you need to know the status of the underlying nail bed. If the nail bed has been badly damaged or has not been repaired well, the growing nail may lift off as it grows out.
Toenail avulsion. Pain, bleeding and infection. You should see your podiatrist to evaluate !
Many possibilities. Pain, redness, swelling, infection, nail bed trauma, and abnormal nail re-growth can result following the “tearing off of a nail”.