The Internet is the easiest route and might save you some
Again this varies a lot depending on where you are going, Los Angeles is cheapest around January due to it being the rainy season so you’ll find the cheapest flights to the USA then, Miami experience its off season from June to August as temperatures get very hot so cheap flight tickets are more readily available if you plan in advance and book them early.
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.