When I have too much anxiety and can feel a panic attack creeping up, one of my symptoms is also a very tight chest and throat. I worry I will not be able to breath! It is just your sympathetic system going into high gear and like Life360 said, it tightens up your muscles. Anxiety does the weirdest things... sometimes I feel like my brain is going to explode and I get blurred vision and weird twitches... tons of physiological things are going on that only makes my worry more. Just know that it is normal and that you are okay.
Anxiety can do many things that cause physical problems. Can cause you to eat too quickly and not chew properly. Your not relaxed and muscles are all tensed up.