There are many ways to go about getting airline ticket
Visit individual airlines’ websites. Although airfare search engines are great, what they don’t tell you is that some airlines reserve their best deals for people who visit their sites specifically. Search for a list of large and local carriers in your area, and then search each of their sites specifically for the best deals. When coupons, discounts, or sales are offered, they will typically only be advertised on each specific carrier’s site and will run for only 1-3 days.
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.