We have a Price Chopper in our area that is open 24 hours and even holidays and I have had to run there before 10 miles away to get stuff because all local stores nearer to me are closed.
2 things that I added to my First Aid kit at home are :
Anbesol Maximum Strength Oral Anesthetic Liquid
Butler G-U-M Orthodontic Wax, Mint
My personal experience with the Anbesol is that it works for about an hour and then you have to re-apply to take the edge off on the pain. The Butler G-U-M Orthodontic Wax saved my tongue from getting sliced up by a molar that broke off and was jagged. I was able to gently push the wax into the hole in the tooth and wrap it over the pointed jagged tooth that kept catching the back side of my tongue making my tongue bleed. This made it easier to eat carefully and not keep stabbing the corner of my tongue into the razor sharp broken tooth. I already had pain pills so I took Ibuprofen to help reduce the swelling around the gum and it worked along with the Anbesol so that I could sleep and see the dentist 3 days later because my dentist was booked up and I was able to get by by this as well as frequent mouth washing with Listerine to prevent infection while the core of the tooth was exposed.
But I was faced with a very expensive dental issue 2 years ago... requiring $10,800 to save my soft teeth that were failing which would lead eventually to them being beyond repair and the cost of $12,000 to have teeth surgically removed and get a full upper denture and partial lower denture and I decided to go the $12,000 route and got my mouth taken care of and saving some key anchor teeth on the lower jaw for the partial to anchor to. Its so nice that the days of tooth aches are pretty much gone now even though I still have 9 lower teeth. Problem with teeth is that 1 bad tooth spoils the bunch like apples and I didnt know that a cavity that I put off because I was too busy was causing attacks to the other neighboring teeth and so in addition to soft teeth that easily chipped, I was setting myself up for failure by not getting a cavity taken care of right away because my job was too busy and I was too important I thought to take time for myself because the company needed me that badly to always live at work pretty much. I was too dedicated to work and not as much myself, but that has changed. I now keep a balance because of the negative affects of living that way, so I'm 44 and dentures and now on a low dose blood pressure pill and more healthy diet.
Worst case scenario is that a hospital is also able to assist with dental problems. Some can fix it there or they can set you up with a way to manage the pain and reduce or prevent the infection until a dentist can get to it. Only drawback to a Hospital is the Emergency Room visit fee that can be rather pricey. There is a walk in clinic in my area that I go to for minor emergencies because with my Federal Blue Cross insurance its just a $35 co-pay and most of the rest is covered. However if I go to emergency room at hospital its usually $300 out of pocket.