Why is my chain slipping/dropping on the smallest chainring when pressure is applied?
You say the cassette and chain have been replaced but the front rings have not. You also mention that the front rings look ok, which maybe so, however it seems there is still a meshing issue between the new chain and older front rings. Assuming the frame or bottom bracket are not misaligned. I would take it back to the bike shop and have them check the chainrings over fully. 
Your not just looking for worn teeth on the rings but the way the chain locates on it.. Even slightly worn teeth can cause issues with a new chain. 
Also check for a loose chain side crank arm or cracked/loose chainring bolt.