Your Mother’s symptom, of “being unable to breathe at night through her nose” must be very distressing. Further evaluation is needed. You state, “Doctors have recommended an ENT and lung x ray for her but the results have come out normal, according to what the doctors say.”
It is unclear to me what this means. Has she had a thorough exam by an ENT specialist and does she or does she not have evidence of obstruction to her nasal passages? If she does, it would seem appropriate to relieve the obstruction with either medication or surgery. If her nasal passages are open then the cause of her breathing difficulty must be sought elsewhere in her body. That when “she talks she starts gasping for breath” suggests that the shortness of breath might even be related to dysfunction of the heart or lungs or related to a complication of the port in her neck.
It would also be important for the doctors to determine if her symptoms are in any way related to the chemotherapy and/or the port that remains in her neck. If her current doctors are unwilling or unable to proceed with further diagnostic evaluation, you should request a second opinion. You should first decide which doctor is primarily responsible for her care and seek his/her advice regarding the best way to proceed from this point. That advice would include the type of specialist requested for a second opinion, most likely to be able to diagnose the problem and recommend treatment.
Good luck to you and your Mother