When I am pedaling hard my chain jumps but doesn’t go to higher or lower gear
Your chain may slipping over the teeth of the cassette sprockets if they are badly worn. This seems the likeliest as the problem occurs when you put increased force on the pedals. Slipping is more likely to happen when on a smaller chainring at the front because the greater leverage is putting more force on the chain. The solution is to replace the cassette. 

Another possibility is that you are getting incomplete 'ghost shifting'. The chain is catching the shift ramps on an adjacent sprocket. This should be fixable by indexing the rear derailleur properly.