She appears to believe you, so I wouldn't worry yet. Prepare for the next test just as if you were still enrolled. Even if you aren't officially in the class when that test happens, you can still take it and she can still grade it.
If she didn't intend to reinstate you or if she intended to insist that you never took the first part of the exam, she would have to deal with an ugly situation with you sooner or later. She'd want to get it over with.
Email her something like, "I want to thank you for reinstating me to the class now that you know that I took both parts of the midterm. Is there anything I can do that might help you find the first section?" That's partly to remind her and partly so that you have evidence later that at the time when the test results were given you were maintaining that you took the exam, she appeared to believe you and she agreed to put you back on the rolls. The odds are that you won't ever need that proof, but it's good to have it, just in case. Print it out and print out whatever response you get.
I would not assume that "If I can't find it by Monday I'll give you an A" is a serious statement. It sounds to me like a way to try to defuse the stress that naturally exists when a student maintains that he or she did a piece of work and the professor believes the student but can't find the work. I think it's more likely that if she doesn't want you to re-take the test (and there are problems with that because you probably looked up the answers to questions you weren't sure about after you took it the first time), if she can't find it she'll probably use some of your existing grades to replace the grade she doesn't have for you. If you've been making all A's, you would end up with an A. If you've been making B's, you would end up with a B.
Let's all hope that she finds your exam: if she was grading on a slightly messy desk, for example, it wouldn't have been all that hard for her to accidently leave the test at the bottom of the stack on the desk, or if she had just finished grading your paper but not put it back into the stack when she was distracted, it might be wherever she was doing the grading.
She probably does have the right, and maybe even the responsibility, to remove a student who isn't doing the work from her rolls. And she had a very good reason to think that you were such a student. Most of the time when professors don't have a piece of work from a given student, it's because the student didn't do that piece of work, and you should take the appropriate action promptly as a result. Occasionally, but much less often, the professor can't find the work because someone (anyone who collected the work and/or anyone who should have graded it) lost the piece of work. It makes sense to assume that if you don't have the work, the work was never done, especially if the student is the kind to blow off work. She apparently was surprised that you appeared not to have taken the MC/short answer part of the test, or she'd just have given you a zero for that part and not said anything to you. So because you are the kind of student who seems responsible, she's doing her duty to you *as well as* doing her duty to the school. I realize that this is extremely uncomfortable for you, but it sounds as if she's doing exactly what she ought to be doing -- and if it's any consolation, this is probably at least as stressful for her as it is for you. You didn't do anything wrong, and she's dealing with the realization that she probably did. That's hard for people: hard enough that cognitive dissonance can convince you that someone else screwed up no matter how strong the evidence that it was you -- and she's resisting the very human urge to believe that she did everything right because she believes in you.
But yeah: write a quick email, just in case. You probably won't need it, but you'll feel better knowing that you have it.