When in the small chainring and smallest cog the derailleur shoudl be almost horizontal. However, you should avoid using the small chainring/small cog combination as this is cross chaining and causes problems. However, the chain shouldn't actually be rubbing on itself as it passes through the derailleur...
Did you remove the derailleur as well as the chain? If you did, it is possible you re-instaled the derailleur incorrectly - so that the b-tension screw (on the back of the derailleur body) is not pushing against the tab on the derailleur hanger.
If you are worried that your chain is too long, shift intot he large chainring/large cog and see how your derailleur sits: the derailleur cage shoudl be angled significantly forward. THis is generally the gear in which chain length is selected - find the length of the chain that goes tightly around the large chainring and large cog, then add two links.. this usually allows you to shift into this gear without jamming or ripping off the derailleur, but is not so long that things rub.
If everything is properly assembled, you could simply tighten the b-tension screw a couple of turns and see if that helps.