My guinea pig is experiencing the lymph nodes inflammation, should i put her down?

Your guinea pig should have been seen by an exotic vet long ago, she is suffering and they can give her medications and pain medication to help her. Sadly it sounds as though you have waited to long and she is to ill to survive, and yes of course the vet will charge to put her to rest. Chances are if you had been working with a good exotic vet through out the guinea pigs life they would not charge you, this is the reason your guinea pig should be seen by a vet yearly even if it has not been ill. The vet then has a report with you and the guinea pig and tent to be more giving.