Fly on multiple airlines. Looking for flights on single airlines may be the easiest, but you may have better results if you look into flying on multiple airlines. Try taking one airline to your destination, and a separate one from. Or, include a layover with another airline mid-flight. Breaking up your trip and splitting it between carriers is likely to save you money, which is worth the extra time and hassle it will cost you.
Use skyscanner.net. This neat website searches all airlines, big and small, and allows you to look for the cheapest rates out of your local, rather than getting bogged down with specifics. Meaning, if you know you want to go on vacation but aren’t too picky about where, this website will provide the cheapest flights to everywhere in the world from the nearest airports to you.
You're not crazy for thinking that a flight price has changed after searching it a few times in your web browser. Based on the cookies in your browser, flight prices do increase when a particular route is repeatedly searched, as the site wants to scare you into booking the flight quickly before prices get even higher. Always search for flights in incognito or private browsing mode to see the lowest prices.