I think I'd go with this piece of advice.

It won't be unsafe to fly as such, but the pain might worsen considerably in the air because the cyst will be able to expand further as a result of the lower air pressure in the cabin. [When you're on the ground, the cyst is expanding, and so causing pain, against a sea-level air pressure (or nearly sea level, I presume); in an aeroplane, the cabin pressure is (roughly) that of 10,000 feet, and moreover, the difference in air pressure comes quickly, over the space of a few minutes, rather than gradually, as it would if you were driving up a mountain, for example.]

So if you fly, make sure you have strong pain killers (not just aspirin or paracetamol/acetaminophen). You might find, however, that the antibiotics reduce the pain considerably over the next few days. I would consider asking the dentist for both strong pain killers and a further course of antibiotics that you could take if necessary while you are away.

I really think, though, from what you have said, that you need definitive dental treatment before you fly. The cyst needs to be attended to, and the tooth either removed or else root-canal treatment embarked on.