Usually the difference I noticed is that when my voice deepens it feels like a part of my throat in the very middle is sore vs when I'm sick it's more like the walls of my throat if that makes any sense. However! During the beginnings of a cold and the beginnings of a vocal deepening I'd give roughly the same advice take your vitamin c (T can weaken your immune system and as someone with an already weak immune system I noticed that during big growth periods [height, bottom, hair, voice, ect] it can be a bit rougher), eat foods like applesauce and soup, stay hydrated, and rest. Hopefully your voice will drop, but if not maybe you'll catch the cold before it gets bad!