Your signs and symptoms point to an underlying periodontal problem. Unless a clinical examination and radiographs are done, arriving at any conclusion would be unfair. Treatment plan, no.of sittings and charges would follow once an accurate diagnosis is made.
Hello friend! Prime reason for gum inflammation, bleeding and itching is bacterial infection of gums(gingiva). The main cause for this infection is accumulation of plaque(soft deposits) and tartar(hard deposits) at the junction of teeth and gums. In this case, it is very obvious that first of all you'll need professional cleaning for removal of deposits, followed by ointments and toothpaste for revival of gum health. Any final diagnosis and treatment plan nevertheless depends on clinical examination by a qualified dental surgeon. Take care. Regards!
The description of your problem is indicating towards a gum problem. It can be solved by a simple cleaning which may cost you maximum 1500/-. In case the problem is more intense which can be confirmed with x Ray you might need a gum surgery or a curettage which may cost you 3500/- to 8000/- per side.
Before all this a simple warm water and salt rinses 4-5 times a day for a week may also solve your problem