Unfortunately, Section 137 at Busch Stadium faces west, so it is likely to be in the sun for much of the afternoon. For late afternoon games, you can expect to find the shade for the last few innings or possibly the entire second half of the game, but for early afternoon games, you may not be in the shade at all in this section. The back portion of this section is covered, so there will be some seats in this section that are shaded for the entire game. Unless you are in about the last 5 rows of this section, you are likely to be in the sun a lot during the game.
I would recommend sitting on the third base side of the field near the left field corner to find a seat that will have a lot of shade throughout the afternoon.