Well water becoming bad with lather and foul smell in every rainy season but turning good in other seasons indicates poor construction quality of the bore well.
Groundwater in hard rock areas where the well is located, occurs both in top soil and in weathered rock under unconfined condition and in pipeline-like fractures within bottom hard rock under semi-artesian conditions. Bore wells are constructed in such areas using down-the-hole (DTH) hammer rigs with casing pipe to prevent top loose formations and top water from entering into the well, while no casing pipe is provided against bottom hard rock for free entry of semi-artesian groundwater.
Because of poor construction quality of your this well, the unconfined water at the top is finding entry into the bore well. Under the influence of the nearby Lake, water table in the vicinity of your bore well in rainy season rises so high as to get mixed up with nearby septic tank waters with E. coli, a strain of bacteria associated with human and animal faecal matter.
These waters contaminate the bore well by entering into it through the annular space between the casing pipe and the top formation. Soon after rains, the water table gets so much lowered as to get disconnected with the septic tank water with little or no scope for entry of top water into your bore well until the arrival of the rainy season once again.
The best course of action would be to construct a grout seal around the casing pipe for a depth of 10 feet or until the top loose formation gives way to hard rock (whichever is higher).
You may study the picture and description at http://www.wbadmorgan.co.uk/info_drilling.htm to know the precautions you have to take to prevent top contaminated water from entering into your well. There is however no need to fix any screen and gravel pack as shown in the picture.
Contributor: R Jagadiswara Rao (https://www.indiawaterportal.org/users/rjagadiswara)