Hi. Thanks for the query.. As per your complain and presentation of symptoms there is a clear cut indication of deep gum infection known as PERIODONTITIS and there seems to be loose of attachment of the gums from the tooth surface due to deepening of infection leading to formation of pockets that again harbours bacteria and causes further infection.. The feeling to press over the gums, poke with something and itching is commonly seen in case of gum disease specifically Periodontitis.. You should consult a Periodontist and get evaluated if your dentist/doctor is unable to find out a solution for you.. The Periodontist will do a proper clinical evaluation and in case of Periodontitis a thorough Scaling of teeth, root plaining and currettage will be done.. A course of antibiotics like Augmentin and metronidazole will be advised along with application of a desensitizing toothpaste and a gum paint.. Chew a Vitamin C tablet daily.. Warm saline gargles are effective.. Maintain a good oral hygiene and do not delay the treatment as Periodontitis can lead to loosening of teeth and in adverse cases teeth may also fall.. Hope this helps.. Thanks and regards..