Calamine lotion. For helping bug bites or itches.
Muscle balm. Creams like Bengay will soothe muscle aches and joints.
Pain relievers. Get both Tylenol and Advil on hand for different uses.
Sunscreen. For stopping sunburns. Another alternative is aloe vera.
Bandaids. Get a bunch of sizes.
Ibuprofen. Treats pain and reduces inflammation. Might be better for sinusitis, muscle soreness, and fever.
Time based cold medicine. Dayquil/Nyquil has high fructose corn syrup, so a healthier option is Alka-Seltzer. If you have sinus problems in particular, you might need a medicine targeted to those issues.
Antibiotic cream. Helps stop infections in minor cuts, burns and scrapes. There are some that even include a pain reliever.
Indigestion. Things like Imodium A-D and Pepto-Bismol can be very helpful when a meal does not sit well.
Allergy medicines. For allergies, a 24-hour non-drowsy antihistamine such as Zyrtec, Claritin etc. is probably your best option. Doctors say certain medicines only work for some people, so keep trying until you find one that works for your (also try nasal sprays). You can also use Benadryl for unexpected allergic reactions.
Rubbing alcohol. Hurts on an open wound but great for sanitizing tweezers and needles.
Cough drops. Cure you sore or scratchy throat.
Canker sore meds. Especially good if you have children, who tend to treat canker sores like painful boils in need of numbification.
Hydrogen peroxide. For small scrapes and cuts. Swab using a little hydrogen peroxide, add on some antibiotic cream, cover with a bandaid, and you are good.
Tweezers. For dealing with splinters.
Thermometer. If you have kids, definitely get the forehead version.