Translation:My teacher has forced me to swim.
It's difficult to explain til at, but it is generally used to indicate the necessitation of an action. So here it would always be tvunget til because someone is being forced to do something.
There are also fixed expressions which use til, such as tid til at [gøre noget] (time to [do something]) or godt til at [gøre noget] (good at [doing something]) but the til isn't attached to infinitive in those cases.
I discussed this further here.