Why does a p-type conduction band have higher energy then n-type conduction band in a p-n junction?
You are on the right lines with thinking about the electrons, but need to consider one more thing:
The energy band diagram of a p-n-junction at equilibrium is dependent on the Fermi Level for each material. The Fermi level is the theoretical energy level at which the probability of finding an electron is 50%. As a p-type material has an excess number of holes, i.e. fewer electrons, the Fermi level lies closer to the valence band. Then for an n-type material that has electrons occupying the conduction band, the energy at which the likelihood of finding an electron is 50% is therefore increased.
As at equilibrium, the Fermi levels must match in a p-n-junction, this leads to the p-type conduction band existing at a greater energy relative to the n-type conduction band.