Wow! This thread *is* all over the map. I am really amazed at all the different passionate answers. I don't know how I missed this for so many days.
To the OP: to answer your original question- if you truly have OCD and were not joking about it then it is difficult to say. You have an unique situation and probably need professional help in handling it. I would guess that carrying wipes is probably helpful, as you mentioned. Also, as has been suggested, keeping your child up out of others' reach. There is no way that you can change others' behavior, in spite of the ranting and raving in this thread, so *you* must adapt. You can only control how you respond and wiping your dd's head and hands is a way to keep her from getting whatever germs the other child may have transmitted. You should know, though, that there are studies that show that too much antimicrobial stuff actually increases the number of resistant bugs and your chances of contracting something truly dangerous, not just a cold.
If you do not have a true personality disorder then maybe you just need to relax a little about germs, realizing, as others have mentioned, that some exposure helps strengthen the immune system. There are several herbal and dietary supplements that will also help, along with plenty of rest, hydration, handwashing, a positive attitude, laughter, spirituality, etc. Unless you homeschool and avoid gatherings of other people of any kind, your child will eventually be exposed to germs and have her fair share of colds, etc.
As far as what I would do, I would not have reacted that way. I would have smiled rather than frowned at the other mother. I might have struck up a conversation with her. Perhaps there would have been an opportunity to tell her something about my child's unique situation if that were the case. She does react anaphylactically to cashews, but it is such a slim possibility that someone will kiss her after eating them, that I choose not to let worry and stress about take a toll on myself or her. Worry and upset can be just as damaging, if not moreso, than colds or allergy symptoms. So far, I have just made a general announcement at parties where there are likely to be nuts.
Just last night we were at older dd's Christmas program. My 20 month old was, of course, not going to sit quietly through the whole thing. She wandered up the aisle and was interacting with the children sitting in front of us. One of them offered a graham cracker. I cringed just a little, but thought better of it. I felt that generosity, sharing, good feelings, etc. were better preserved. If I had intercepted I would surely created bad feelings, and not necessarily prevented anything bad as far as dd's physical health. As far as personal space goes I did a little experiment to see what they would do if she invaded theirs. To my amusement the one little boy, probably about 8, just lifted her up under arms and deposited her back out into the aisle when she crept too far into their seating area.
She also received hugs and kisses from another toddler. That child's mother also laughed and said "She wants to hug and kiss everybody." I laughed, too, and we chatted a few minutes about our dd's and their different personality traits. I think if the other child had been older, bigger, rougher, etc. I might have squatted down next to dd and helped her deal with the situation. I think that while our children definitely have hard wired personality traits, they also gauge their responses by our own. When they fall, if we do not get overly upset and rush to them, we may see them pick themselves up and keep going. If they get a rough hug that surprises them and they whimper a little (or even shriek!) and look to us to see how we respond, we can say "It's okay. Did that surprise you? He is very happy to see you! Do you want to hug him back? Or would you rather shake hands? Or maybe Mama can hold you while you talk with him." You could also speak to the child and ask him to blow her a kiss (LOVE that idea!) or to just touch her feet. I realize that in your case he ran off quickly, but you could still respond to whatever your daughter was doing. And in response to his mama you could have told her whatever pertinent information is appropriate. Like she has a weak immune system, or you hope her child is healthy, or whatever.
Really, though, I think your best bet, barring tempering your own response to the germ issue, is to keep her out of the line of fire. Keep her out of WalMart altogether or keep her up out of the way in a cart or sling.