I've tried using the smooth tool in sculpt mode, and while that does seem to fix the problem, it also ruins the overall shape of the edge by rounding it off. Do I have to retopologize this mesh altogether or is it saveable?
Although retopology would be the best/most logical solution here, you could try to use the
pinch tool, which pinches/squeezes geometry, and hold Shift to do the reverse (spread out/smooths the geometry out). A subdivision modifier here would be impractical since your mesh is already pretty dense as shown in the image you've provided.
If the pinch too doesn't, I suggest you go straight to retopology. It's good practice to do so.