Can I add bookings I made offline with the airline myself into the travel agency software so everything is in one place?

Yes, in most cases you can enter an offline booking by hand so it sits alongside the ones made through the system. Plenty of agencies still take part of their business over the phone, from a consolidator or straight from an airline or hotel desk, and that work needs to appear in the same place as everything else. A manual entry normally lets you record the passenger name, the travel dates, the supplier, the booking reference and the amounts you charged and paid, and then save it as a proper booking in that customer's file.

What you should expect, though, is a record rather than a live connection. Because the booking never went through a supplier link, the software has no way to check its status with the airline or the hotel, so it will not update itself if a flight time moves or the supplier cancels. You stay the person who watches that booking and edits it when something changes. Tickets and vouchers for offline work usually have to be attached as files rather than produced automatically.

Whether manual entry is available to you, and how much of it your staff are allowed to do, depends on your plan and on the permissions you set, so it is worth checking before you rely on it for a large part of your sales. The same applies to whether those offline bookings flow into your sales reports and invoices, since that is what most owners actually want from putting them in.

The simplest next step is to enter one past offline booking as a test and then look at your reports and invoices to confirm it shows up the way you and your accountant expect.