The anxiety is typically caused by the defense mechanisms in the body trying to block the retrieval of an emotionally traumatic memory when something in the current environment is stimulating retrieval.
For example, the tightening of the inter and outer costal muscles in the chest blocks the afferent spinal nerves from transmitting emotional discomfort to the central nervous system. This is one of the reason that stellate ganglion nerve block shots and the placebo stellate ganglion shots both work for PTSD treatment, but only temporarily. I talked with the researchers at Walter Reed about this and was not impressed.
The chest muscle contractions give that compressed chest feeling and make it difficult to breathe during the anxiety attack.
Yes, anxiety can cause a choking feeling in the neck area as well. EMDR is good for helping releasing physical body memories. But, as I stated before, anti anxiety is an excellent medication to help a person who is in severe distress and allow them to process when they are ready. You can not push a person to process more than they can handler before they are mentally, physically, emotionally ready or it could make someone much worse & backfire. At that point the therapist may spend weeks to months just to get the patient back to a somewhat stable place to begin working on the memories which sent them there to begin with.
Also, the anxiety causes the tightness first. Then the tightness causes anxiety. Tools are used to break the cycle. Sometimes meds help.