Prices really do change depending on the time and day, that's actually true. Comparison sites like Skyscanner and Kayak still work well, but you need to understand how they operate so you don't get paranoid thinking you're being scammed. These aggregators pull information from airlines and travel agencies in real time, so the price variations you see are genuine - the price changes because demand changes, fuel fluctuates, and airlines adjust constantly.
The trick is to use these platforms to get a general idea and compare, but then go straight to the airline's website to confirm and buy. It's not that the sites are bad, it's that they make money from clicks or redirects, so sometimes they find deals that the airline is testing. For September specifically, the ideal thing is to start monitoring now - set up some alerts on Skyscanner and keep track. If you see a good price, go directly to the company's website (TAP, Azul, Gol, whoever) and check if it's the same. Usually it is, and you feel safe.
The "being scammed" thing you're worried about basically doesn't exist in these cases. What happens is that whoever waits too long misses out on deals, and whoever books during peak hours pays more because everyone's looking for flights at that time. A tip from someone who's dug into this a lot: fly to September on a Tuesday or Wednesday, avoid weekends. That's when you actually save money.