If you are traveling it is very important to read carefully the new laws of airports and what is allowed on the plane. The new laws are very strict and if you take something in your carry-on luggage it can be taken from you at the airport.
One of the safest ways to avoid issues at an airport is to buy a pre-made bag that has the correct amount of liquid in each container that is allowed on the plane. You can normally buy these in many markets today.
Pack the rest of your items in your suitcase when you travel. Don't try to take half used bottles on the plane. They should be in a clear plastic bag or a ziplocked bag so they can easily see what you are taking on the plane.
You can easily make your own bag from items that you have picked up in hotels. Many hotels will give small bars of soap, shampoo, toothpaste, and a toothbrush. Use these items and put them in a ziplock bag. They will easily pass through all airport security checkpoints. If you are traveling light and don't check in your luggage then you should use do this. Once you reach your destination you can purchase anything else you need there. However, you'll need to throw them away before returning home. These items will not pass airport security for sure.