I was in a car accident recently and went to a physical therapist. I complained that anytime I did pushups my left shoulder would feel numb, or irritate me for a day or two afterwards. He explained the same thing everyone else is mentioning. My back muscles are weaker than my chest and arm muscles, so I'm straining my neck/back by doing too much too soon. He gave me a simple routine to strengthen my back/neck first. It really helped a lot. He also mentioned that this imbalance was connected to the fact that I had bad posture while sitting (shoulders rolled forward.)
If you ask me, your mentality is all wrong. This whole idea of being embarrassed, or trying to put up as much weight as you can. Are you trying to compete for weight lifting, or body building? If not, I don't think you should be embarrassed, or worry. You're pushing yourself for all the wrong reasons. You should do what benefits you the most, not what impresses others.
I suggest dropping the weight significantly for a while and focusing on building your back muscles with rows, shoulder blade squeezes, etc. Your shoulders can be built separately as well using things like military presses. If you really wanted to, you could do an experiment and do just pushups for a week. It takes 2 weeks to start losing muscle anyways, so you won't be in any danger of that. If your shoulder is still bothering you from pushups alone, your back muscles are WAY weaker than your chest muscles. You need to focus solely on back/shoulder/neck for a while and start small (maybe no weights at all).
I don't know what expectations exist that you're applying to yourself. Where is there a rule book that says every man should be able to lift X weight, or have X" muscles? Just be you, and lift the weights that accomplish what you need to accomplish. Muscles require a ton of food (costs money, takes time), they weigh more than fat (makes you heavy, bulky) and not everyone is attracted to them (I know more girls who don't like big muscles than girls who do). Honestly, muscles aren't by default the greatest thing in life. If you have a specific purpose for them (i.e. You're running, fighting, etc.) then build just what you need to be excellent at that activity. Otherwise you might be over-doing it. Just my two cents. It's your life.