I had this too several years ago....even went to a doctor to see if it was anything. All they could say was "probably hormonal changes". Yeah, duh! I could have figured that out by myself for a lot less than a doctor's visit. Also went to have a mammogram (NOT fun ever but even less fun with a sore breast!!!!!) Nothing showed up.
You might have actually pulled some muscles in that area. I know, it seems odd to think that, but it's possible. Like any other place in the body, pulled muscles may take awhile to "heal".
With children around, this is tough I know, but just try this home remedy: Several times a day, place a pretty warm compress (not quite hot but not just lukewarm either) on the tender place. A plain old washcloth will do fine :) You can do this quite easily if you like taking baths. If you're more of a shower person, you can direct the spray onto the affected area. But best of all is the compress directly on the spot.
Try switching to a different antiperspirant. You might be having some mild reaction to the one you're using. Sometimes we can build up intolerances to products. If possible, try a deodorant only....one without aluminum chlorohydrate. Or best of all, check out one from a natural foods/supplements store.