There's no such thing as senseless violence, according to the one who commits it. Characters who kill or torture without at least an internal justification are crazy, not evil. You don't have a reason to kill people in the party or at random, so you don't. This doesn't make you nonevil.
Also remember that just because you're Evil doesn't mean you're a villain. Many Evil characters have no ambitions higher than their own survival and/or comfort; they don't aspire to great power, nor to purge the world of the target of their hate. They're just trying to get by, not so different from the rest of us.
The traditional list of Seven Deadly Sins was originally compiled not so much as a list of inherent sins, but a list of reasons that people sin. This makes it a great source of motives for Evil characters. I prefer to expand the list to nine, adding Fear as Wrath's twin in the fight-or-flight reflex, and Despair because it was actually in the original list; Sloth replaced it later.
Avarice: The key to happiness is having things. I will have it all.
Envy: I deserve it, not them. I will have it from them.
Gluttony: Pity those not at the top of the food chain. I will never be in that position.
Lust: I want to do it all, and I will let nothing get in my way.
Pride: I must be better then them: so much so that my superiority is never even questioned.
Sloth: I just don't want to do it. Let them do it for me. If they refuse, make them do it for me.
Wrath: They will never hurt me again. I will punish them for what they did, and leave them unable to do it to anyone else.
Fear: They must not be allowed to hurt me. (Note the lack of an again here: this is one of the big differentiators between Fear and Wrath, but it can make a huge difference in the character).
Despair: I just want the pain to end. Giving it to others helps.
Also keep in mind that these are core motivations. Any one of them will need to be elaborated upon. What is it? Who are they? How does the character plan to achieve this goal? Also worth noting is the lengths that your character goes to to hide her motives. Evil characters often prey upon one another's weaknesses, and while Wrath-type characters might not worry about seeming weak due to their motives, Sloth-type and Fear-type characters likely would. These folks are likely to construct a facade, often but not always based on Wrath, as a matter of posturing.
Your character sounds like a Wrath-type, with a focus on the undead. Because her main focus is on something that is not so amenable to the survival of humanity in general, she can get along decently well in society, and even be a very useful sort of person to have around. Some might even mistake her for heroic. But she has a twisted fight-or-flight reflex: any slight or injury, real or imagined, runs the risk of touching on that trauma, for reasons that make sense only to your character (if they even make sense to her). She might lash out disproportionately at small threats, or even against things she mistakenly believes to be threats, but are not.
Best Answer
Limb loss is not a part of the game, there are no rules for it, and a DM who houserules it in is responsible for deciding what that means and how it is dealt with. Regeneration and the ring thereof are the only references to the idea, and they heal something that cannot happen. It's pure legacy cruft. The third edition of the rules went much more for the style of “fantasy heroics,” and does not want or need to accurately model injury in combat. Combat is the focus of the game and part of the fantasy is that these realistic risks are not risks for our great heroes or dastardly villains.
Furthermore, such a significant change to the rules relative to the default, not to mention the tone and style of game, should be announced ahead of time, as part of the premise of the game. You should already know the answer to your question, because your DM should have explained his homebrew limb-loss system to you before you made characters.
This is doubly true if your DM is using the lack of rules in this area as a “gotcha” response to your playing an undead character, which it certainly seems like he is. Did he tell you he was using houserules that included loss of limbs? Did he warn you that this was a weakness of playing an undead character when you brought the idea up? Because he very much should have, as this risk is not one present in the default game.
If he did, you might be out of luck; I think it’s a pretty poor thing for the game overall, but if you were aware of the risk and accepted that, well, that was the risk you took. I would strongly consider retiring the character at this point, however. A cripple does not make a good adventurer. It does depend on your class and such just how crucial it is, but most classes are going to struggle to the point where continuing an adventuring career would be suicidal.
If there was not warning, I would ask him what solutions are available, ask him out of character to provide a way for my character regain the use of both arms so that we can get on with whatever we were doing before you got crippled. A side quest or something. If this can be resolved, then fine, it's a part of the story and can be fun. I’m all for cool stories.
But with no warning, no communication of the change of rules and tone, and no opportunity to undo the damage, there’s a major problem. Your DM has introduced a massive, permanent, and unannounced change to a player character. If he just expects you to have this massive (and undefined) drawback for the rest of the game, I would consider that a major abuse of DM authority to spring such a large change on a player's character. I would at that point strongly consider leaving the game. This would not be a game I think is worth my time. Not really because the loss of a limb is unplayable necessarily, plus retiring the character is always an option, but this is a sign that this is a DM that oversteps what I consider his bounds to be, and is likely to do it again. I’m not interested into playing in a DM’s power trip.