Upvote:1
As you had a paper ticket, one might guess you booked through a travel agency, who may still have your information in their reservation system.
Sri Lankan Airline will have your booking/ticket data in their system and can likely look it up for you (perhaps with a fee involved depending on how long ago you flew). They would likely need your PNR (record locator / reservation id), last name and perhaps a third identifier (credit card used, first flight number, date, etc)
If you had the flights credited to your frequent flyer account, you can look up dates, flights and perhaps fare class through your frequent flyer account.
But as a general rule, airlines do not maintain online records of past flights through third parties. Nor do they make them easily accessible through their public website.