I had to look up black spot as I had never heard of it. The site I looked at said black spots appeared when a fish was healing from ammonia surges. Or from pigmented cysts of intestinal flukes but these appear on body and fins, not the ends of fins. The white string poo indicates something internal though. What did they give you to treat it with?
Good to hear it has recovered. Diagnosing sick fish can be difficult and often, by the time it is showing symptoms, it is too late.