This is such a typical problem with silver,when its not worn and getting gently rubbed by clothing,you etc it does have more chance to build up,and it can almost look like rust!!
I have tons of bits of silver jewellery,and I don't wear them anymore,so they do get very tarnished.I have used silver dip in the past on them,as it gets in all the nooks and crannies more effectively than a cloth. I have started putting them in little grip seal bags once they are fully dry,and they don't tarnish hardly at all now.Its the atmosphere that causes it so its fairly unavoidable!
I do use a silver cloth when I have dipped them as it brings up that lovely new gloss,but as the cloths are ever so slightly abrasive,give your jewellry a rinse under a warm tap and you won't get any residue when you wear it next.
Your earrings are more than likely rhodium coated so thats why they will seem to have escaped tarnishing,also if you wear them pretty regularly it does'nt have chance to build up.
Following the advice of one of the other posts,take them back and get them to explain or show you what to do,they really should have told you when you bought them so this situation would'nt have cropped up for you!!!xxxxxxxx