Another thing to note when you're booking your flight tickets online is to consider extra fees and "hidden" charges such as credit/debit card fees, baggage, meals, certain seats, extra leg room et cetera. Factor all these in before you compare between different airlines and flights before making the final purchase. Most online travel portals require you to pay via credit card, and may charge you a hefty credit card fee. But some sites also accept PayPal (including American Airlines website aa.com, Agoda.com, hotels.com). If you buy tickets directly from most airlines, you also won't be charge a credit card fee, and you should take those charges into consideration when choosing between booking through an airline website or other travel websites. Some online travel agencies let you pay via wire transfer from your bank account.
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.