Could you explain why does my jaw lock after a certain point on the left side?

Jaw locking: The TMJ is a very mobile joint and the disk in the joint is very mobile as well. The disk is often out of proper position, as the disk attachments may have been stretched. What you feel is the jaw bone sliding over the displaced disk, a "catch" often with a popping noise as you open. The management of TMJ disk problems is usually conservative unless pain or decreased function or locking is severe.