I would highly reccomend you get good at Dips.
Do them INSTEAD of bench press (or whatever your main chest exercise is) every 3rd workout, and do them last in the other two workouts. Make sure that you are not gripping too narrow or wide. To get better reps out, concentrate on keeping your entire upper body tense and contracted throughout the entire range of motion. Do not go down for a full stretch. Go to where the arms reach about 85 degrees (so just 1/2 inch past parallel to the floor. When your shoulders get used to the stress you can go lower. Do not lock out forcefully, move quickly for near lockout to the next lowering phase.
Fact is, if you can get over the problems that you have with the dip then you will have taken your body to the next level. Dips are actually like an upper body squat. They are a key movement and unless you have something like a torn rotator cuff then you dont have a good excuse - just because you are not good at them is not a reason.
I SUCKED at dips for years so I didn't train hard at them. Now I love to hate them. I use them as a killer finisher after presses and flying movements. I can either strap weight on if I feel powerful, or do high reps (like 30+) at bodyweight.
To get good at dips, when doing the FIRST in your chest workout, do as many sets to mometary muscular failure, as it takes to reach 50 reps, example:
12 reps
10 reps
9 reps
8 reps
7 reps
6 reps
When doing the exercise last, just do one or two sets for maximum reps.