You may need a longer chain. By changing to a larger rear cog the overall circumferance of your drivetrain is larger. This means you may need a longer chain. Shift into the big/big combination. Is you chain taught or is there some looseness to it? If its taught you need to go longer.....
Just remember you only need a link or 2 longer, any more than that may give un-wanted slack in the small/small
1984 Schwinn Paramount; 1987 Schwinn Paramount; 1975 Tom Ritchey, 198X Vitus