Sheva,
You made some observations that are important but I need to ask you to qualify some:
1) The water level is High due to rain. Is it more than 1/2 way up the skimmer's mouth?
2) Was the water you saw gushing in the skimmer as the skimmer was emptying and it's water level dropping faster than the water could get in or was it just in the pump?
Fiberglass pool shells are typically formed with the walls slightly pitched back to be less than vertical. This also tilts the skimmer body since it's attached to it. This reduces the normal operating water level from 1/2 up the skimmer to something less, usually about 1/3 of the way up the front. Further in the skimmer mouth, because the body is tilted back, the level reaches the flapper at the 1/2 way mark.
Sometimes, when the deck is poured, the skimmer flexes slightly under the weight of the concrete. The flexed mouth sometimes catches the top of the flapper in high water conditions. This can cause a dam to form, preventing sufficient water flow to enter the skimmer. The dam is not water tight so some water gets in. Since the water level in the skimmer has dropped, the water that does get past the weir/flapper appears to gush.
Freeing the stuck flapper resolves this until the water level rises again. I usually test the flapper in this situation by putting a pool pole in the skimmer mouth on the pool side and giving a gentle push on the weir to free it. If the homeowner says it's intermittent, I will reach in the skimmer and lift the flapper to check for freedom of movement. If it gets stuck near the top, I know the cause is either the wrong weir or the concrete flexed the skimmer housing.
If its a Pentair skimmer, I remove the flapper and install a floating weir in the skimmer basket. All others, homeowner awareness is the only solution that I know of.
If the weir is free and the drain is closed and the pump is still starved for water, it is possible that either a clog exists or, if the installer used flex pipe, it is collapsing under the weight of the strength of the suction, forming a kink in the line. Eventually, the creases in the kink will create a hole in this line.
A pressure test will not find a collapsed suction since the pressure in the pipe is the opposite type of what is causing the kink. In fact, it may remove the kink temporarily. Kinked lines must be replaced.
This situation is also one of the two main reasons why I don't like flex. The other reason is termites can/do eat flex.
Scott