SQ has an excellent lounge at Terminal 3 with shower facilities. With a 3 hours+ connection, you have enough time to use the facilities to freshen up and explore the airport. You can easily explore T1, 2 and 3 using the skytrain (T4 is small and not connected to the skytrain). If you are travelling between T2 and T3 using the skytrain, you will pass through the Jewel and the rain vortex.