It does sound like the system needs to be bled, but its easy to do. Make sure the reservoir is full and turn it to the stop one way, hold it there a few seconds and do the same for the other stop. Shut it down and check the fluid. It will probably be all foamy and low. Fill it up and keep doing this until it turns smoothly from lock to lock.
I agree, a reputable mechanic should not have let you go out the door this way. I hate to say it, but you probably didn't really need a gearbox either. I've never had good luck with mechanics and steering trouble, always wound up fixing it myself.