A Shiva Lingam dream can have the following three meanings:

Usually if any God appears in our dreams, it means that their temple should be initiated nearby.


Other meaning of dreaming about a Shiva Lingam means that something bad that was coming your way has been removed. Since he swallowed the poison, similarly, he swallowed your problems.


Third meaning of the similar dream is that you might need to go out, find a nearby Shiva temple and bathe the Shiva Lingam with milk.


Every dream can have various meanings. It depends upon which  one suits you the best.