thanx for sharing your concern.
i can understand how it feels when you have a very mobile teeth in your mouth.i would suggest you try not to disturb it because it might bleed profusely on plucking,also there could be associated pain too which can give you sleepless night.so try and avoid.
you can seek your dentist
help in this regard.
you have localised periodontitis
.the features of periodontitis are mobility of teeth,deep pockets,surrounding bone loss etc.
you need to visit your dentist.Get an OPG radiograph done.this will show you, the condition of your teeth,underlying bone support,bone loss,and also presence of infection.
after judging the above symptoms,and its severity, your dentist can decide whether you require periodontal flap surgery,currettage,and bone graft etc.
this will surely help and improve your gum prblems.till that time maintain good oral hygine.