I get a tight feeling in my chest and start feeling very anxious everytime my family eats food around me, almost hateful. What could this indicate?

It sounds like. you may have an unhealthy relationship with food. For some reason this is stirring anxiety & anger. If you need help to get to the bottom of it, considering working with a good therapist.
Anxiety. This indicates that some sort of anxiety problem is present, but the nature or further details are not clear. You would be wise to get a full evaluation from a mental health professional.