Braking While Turning

The simple answer to the question in your subject line is "no", you should not be braking through a turn.

By the time you begin making the turn, the truck should be under control and moving at a safe speed. Which means in a manual you should be in a gear no higher than 3rd.

Although I agree with the others to relax, don't overly stress over it, there is a lesson, a take-away from what you experienced. It's preparation and having a plan before reaching the intersection. Be prepared to stop and/or slow down before reaching any intersection, off-ramp or stop sign.

Try to get in the habit of planning your moves in the truck before you actually need to execute them.

Nerves...don't let them get the best of you. Good luck!