Part of first aid training is teaching you to always be prepared in the event of an emergency. That does not mean that you have to walk around with a loaded doctor bag everywhere that you go but it does mean that you should have a few functional first aid kits in specific locations such as one in your home and maybe one in your car.
You can buy these kits pre made but you might find that they do not have everything that you might need in them and you will have likely paid more than you should for it. In first aid training they will give you a list of things that should be in your first aid kit. There is a lot more to a functional first aid kit then a few band aids, a couple alcohol swabs, some gauze, and adhesive.
A well put together first aid kit should include the following items: absorbent compress dressings, numerous band aids in various sizes, adhesive tape, antibiotic ointment, antiseptic wipes, aspirin, a blanket, a breathing barrier, an instant cold compress, non latex gloves, hydrocortisone ointment, scissors, roller bandages in different sizes, sterile gauze pads in different sizes, an oral thermometer, triangular bandages, tweezers, and a flashlight...