Getting a little string buzz - fret rub

I have an ESP LTD M50 electric that I bought used. You can tell its been around the block a few times. But, it has a thin neck, low action and I can play it (I have some carpel tunnel in my left wrist and have problems with a thick neck and/or high action).

I'm getting some string buzz on a few of the stings when played open. I do not hear if I just give the string a light pick. But, a harder pick will produce the buzz. Upon closer examination I found that a hard pick on some of the open strings will cause them to vibrate against the first fret. I can even see wear on the fret where this has occured over time. That's probably why I don't hear it when I'm freting a note and hear it on open strings. So, it looks like the vibration against the first fret is what's causing the buzz.

What to do about it? New strings? See if a shop can raise the action a little? Do I need to have that fret replaced?

Hi Irma. I'm new to the forum and only just saw your post..you have probably got it fixed by now, if not it sounds a classic case of changing the "Nut" and cutting it right...A decent luthier should do it without to much cost.

Fenderphil