Sounds like you may have 2 problems:

1. Somehow, your skimmer basket is obstructing the flow. This shouldn't happen if it's (a) clean and (b) the right basket, so I don't know how it's occurring.

2. If you are getting air in the pump basket, you have a suction leak. Period. If you didn't have a leak, you wouldn't have air. But if you have a SMALL leak, it won't show up on a flooded suction pump (below water level) UNLESS something obstructs the flow upstream of the leak location.

The most common locations for a suction leak are the pump strainer lid gasket, and the point where the piping is connected to the pump. BUT a suction leak can be *anywhere* between the pool and the pump.