To check for leaks: Dry the pipes with a rag before testing for leaks. Turn on the water and check that you don’t have any leaks under the sink. Run water in both sink basins for a couple of minutes each.
To be sure that your pipes will hold, you need to run a larger amount of water under pressure. Use the stopper to fill each basin at least half full then watch for leaks when you pull the stopper out.
If removing the trap doesn’t clear the clog the next step would be to snake the drain.
