The OP's desire is to have indexed shifting at the brake levers...aka brifters. This is assuming the Schwinn's drop bars are to be retained. 7 speed Shimano and possibly Microshift, brifters are available. You will need to upgrade to a 7 speed freewheel, chain, and index compatible rear derailleur.

There is a more economical alternative if changing the drop bars to a flat bar. You can use mtb/hybrid shifter/brake lever combos. You gain indexed shifting at the brake lever without costing an arm and a leg.