I don’t know. That’s going to depend on the specific scars and what damage the original wounds did.
Burns can do all sorts of nasty things to your character’s tissue. Scars aren’t likely to do much on their own, though the original injuries could have severed tendons, cut nerves, or just carved up the arm.
So, really, the question you should be asking is, “what happened to her arm?”
Nerves that have been nicked by a blade (or claw, or bite) can result in dead patches further down the arm, or on the hand, that no longer have a sense of touch. Severed nerves can result in partial or complete paralysis of the affected limb, and this is stuff that does not heal.
I’ve, fortunately, never had to deal with a burn more severe than specs of flying cooking grease, so I’ve forgotten a lot of what I learned about burns. But, here’s the thing I do remember (outside of rare circumstances) burns that are severe enough to scar transition into immediately life threatening very quickly. Second Degree burns can scar and require skin grafts, but anything past that will probably kill your character if she doesn’t get medical attention, and medical attention will probably include lopping off the arm.
For reference: First Degree is superficial, without blistering, Second Degree is superficial with blistering and/or cracking of the skin, third degree is a deep tissue burn, and fourth degree is fully cooked.)
On the personal experience front, my left thumb is actually a little numb as I’m typing this. I burned it on a frying pan about a week ago. There’s no visible scaring, though it’s actually somewhat possible I’ll never get full feeling back. Just, you know, food for thought.
I’ve also been on the receiving end of an electrical burn, once. (Technically, it was about 11% of the voltage you need to actually classify for an electrical burn. But, it’s easier than saying, “I got shocked.”) The thing that stuck with me was a tingling sensation. For about a week after, felt like the fingers were twitching, even when I could see that my hand was (basically) still.
So, yeah, burns are not happiness.