Julia,

Can you buy the tickets through the airline themselves? Via their website or something? I used to use third parties to book my tickets but anymore it's usually cheaper to buy directly through the airline because the third parties, of course, add on their fees.

Maybe you know already, but Google has a useful page for checking flights.

flights.google.com or just type Google Flights into Google search and it will come up.

You can check the prices of various different airlines and also see when the cheapest flights are each day by clicking on the month. The results can vary a bit from what you'll actually pay but it will at least give you an idea of prices.

I hope that helps you a little.