Traveling on the road and getting sick is no fun. Sometimes it is the price to pay for going out on a lot of overnight trips. A little bit of preparation can make it a little less problematic.
When I am traveling on the road I like to have a medicine kit and a first aid kit, more or less depending on the destination and the amount of medical care and support I can find nearby. It also depends on whether I am in my truck with a lot of gear or if I am traveling in the mountains or backcountry with just a backpack.
I have a standard first aid kit that I purchased for around $30 that includes ointment bandages and other simple tools for first aid and a pouch full of over-the-counter medication.
For medicine, in a similar soft-bag, I carry the following:
Tylenol
Advil/Ibuprofin
Gravol / Anti-nauseant
Immodium
Benadryl
Tylenol Flu +Cold Extra Strength
Throat Lozenges
Emergen-C, or some kind of electrolytes (Gatoraid is often what I find last minute)
Topical cream for skin/fungal infections
Antacids
Deet Bug spray/cream
Sunblock 50 SPF
Superglue for small cuts
Add to this list any specific medication or prescriptions that you need, perhaps consider taking an additional buffer or near twice as what you would expect to use.
During my time working as a photographer for a raft guide company, I remember seeing helicopters fly over to medevac out people who had been hurt on wilderness outdoor travel rafting trips. Consider reviewing and double-checking your travel and medical insurance and consider medical evacuation insurance.