I second ITA Matrix as the greatest site for looking for fares. One thing to remember....Southwest is only allowing bookings through August 10. According to their site, they'll open more dates on March 12. This could lead to lower fares across the board as more capacity is suddenly available.
The matrix and google flights are total proof that you don't need to clear cookies when looking for flights. They won't be more expensive for you on an airline website than you can see on either of those pages. If you see fares go up, they're up for everyone, not just you since you went back to an airline site. I work on a computer, so when I'm looking for a flight, even if it's 6 months out, I'm refreshing the page on ITA Matrix every other hour or so while I'm working. I was looking for flights from Newark or Philadelphia to the LA area for August and bought flights last week when United dropped their price....5 times in 48 hours, from $195 to $140 one way...then down to $120 after four $5 drops. Would have been about $90 for basic economy, but I won't deal with that. I cancelled (within 24 hours of purchase) with no fees and rebooked their $5 drop each time. None of the other airlines matched, so the prices went back up the next day.
Bottom line....look OFTEN on ITA Matrix and always for just ONE flyer. Play around with the different parameters and sort options in the results. You never know when the drop you need will hit and you need to be ready when it does....then keep looking for the next 24 hours to see if you can improve your tickets. If you need 4 tickets and the airline has 3 available at $150 and the 4th would be $180, make two sets of reservations. If you put all 4 on one reservation, you'll pay $180 apiece for all four people. That's why you always want to search for one to start.
Good luck!!