Sesame doesn't have to be listed on food labels so if a label says any word you don't know the meaning of or that can mean multiple things like 'spice', 'natural flavoring', 'flavoring', etc you would need to contact the company and ask whether it has sesame or not. Some companies will tell you and some won't.
Bread is the biggest thing to avoid IME. Most in the USA are produced on the same equipment with sesame and can have sesame cross contamination. Crackers, salad dressing, soups, almost all Asian food (and I'd say all Asian restaurants), even something like canned tomatoes can sometimes have sesame! Cereals, of course hummus and other Middle Eastern foods and restaurants, many types of pretzels and more frequently have sesame. Also, corn chips, some salsa, bread crumbs and more.
It is difficult to avoid but more and more companies are at least aware it is an allergen.
When I called Amy's they told me that all their flavoring is made in the same room where they make things with sesame and there could be xcontam so we avoid their stuff. I love their company, though. Maybe they have changed but I recommend calling them to check how they handle sesame and the chance of xcontam.
Nabisco/Kraft and Cascadian Farms and a few other companies (Pepperidge Farms?) treat sesame as they do top 8 allergens and label for it including if there is a chance of cross contamination. Maybe Keebler has changed but when I contacted them in the past they would not give me any information about sesame so we avoid their products.
Chipolte, Red Robin (YMMV), Papa Ginos, Burger King (only their fries), places that cater to gluten-free people, some other pizza places have all been good choices for us.