For kids older than that -- kids that are six months of age or older -- it's safe to do Tylenol or Motrin, or acetaminophen or ibuprofen, but those are based on the kids' weight. So it's a little tricky to know at home how much to give. A good question to ask when you go in for your routine child care is "What doses would my child need? Something to help with pain in between our next visit -- what dose could they use?"
As far as older children go, there are over-the-counter allergy medications that are safe. There are antihistamines such as Benadryl that are safe. The over-the-counter allergy meds are things such as Zyrtec, Allegra, Claritin -- those are the brand names that people are familiar with.
Sometimes people will give medications for gastrointestinal (GI) upset to kids. Tums is one that you'll sometimes use for older kids, but I would certainly stay away from things such as Pepto-Bismol -- it has an aspirin component in it. You never want to give aspirin to a child, because it has been linked with something very serious called Reye's syndrome. Again these are questions that you would ask your health-care provider because so much of what we do in pediatrics is based on a child's weight and age, and a generic answer would not be helpful for you.