The Sword and Laser discussion

I am trying to find an old(er) book in the fantasy genre that I only vaguely recall, but do remember liking. I am hoping someone else here in S&L has a little better memory that my swiss cheese cabeza. That, and my Google-Fu is lacking lately, I guess.

Please, if you can help, point me at this book. I'm curious if the author ever wrote more, and if it's as good as I remember it being.

The details which I remember:

1. The heroine & POV is a transplant, from modern Earth to a magical reality. She can hear the gateways between worlds as an ear ringing that is diagnosed as tinnitus.

2. Her gift for magic involves painting. There is a significant bit about magic in parchment, scraping hides, the durability of skins, etc.

3. The love interest hero is a roguish fellow, reminiscent of the Han Solo archetype. Due to weapons controls the fighting in "civilized" territory tends to be knife duels (very specifically, swords were heavily controlled)

Thank you, all.

The Barbed Coil ?

Thanks, Tassie Dave, that's it. I've been looking off and on for weeks.