Nah you're not a wuss. You prob have either a technique problem or a joint imbalance.
I get it in my anterior deltoids. They're getting too strong in relation to my back, so when I bench they tighten up. To relieve it, I stretch my pecs and shoulders before, during and after bench press. This is suppose to decrease my strength slightly, but I'd rather be a bit weaker and pain free, than strong and immobile in my shoulders.
Without seeing your technique, it's difficult to give advice. Try to think about the way you are doing the exercise, what muscles can you stretch to relieve the pain? Are you following an imbalanced program (more push than pull)? If so, maybe reducing the volume on chest, increasing the volume on back and stretching the chest to reduce joint tension is all you need to do.
I wouldn't recommend just sucking it up and blasting through it. The pain is there to tell you that something's not right.