We all want the best for our kids, and we all hate to see them hurt (physically or emotionally). But you're actually making it much worse for your son by doing what you're doing.
So, ask yourself why you do this. Do you think that any problem or failure he might have is a reflection on your and your parenting? Does a kid skin a knee or get a C- on a report card or have a fight with his friend because his mother failed? Is this possibly about your own insecurity or your need to prove to yourself and/or others that you are on top of every possible bump in his life's road? Is it a measure of your capability if he doesn't confide every detail of his life or share every problem with you? Were you neglected in some way and perhaps hold this against one of your parents?
Or is your concern truly and solely for him, that you're afraid he might experience the not-so-fun things that happen to all of us? I'm going to guess that it's not all about him - that it's either all about you or that it's combination. So, for the part that's about shielding him from pain/hurt/depression/bad days, what's your plan for his future? Do you plan to go on dates with him and move into an apartment with him when he goes to college? Do you plan to go to his job interviews with him, call his boss about a raise, be with him when he proposes marriage, go on his honeymoon? You'll probably say, "Of course not." To which I would reply, "Then at what point do you think you will stop this behavior and let him live his life?" There's no logical stopping point in your mind. How in the world will he ever learn to be an adult if you don't let him be a mildly independent kid?
The problems here are two-fold: your son is quiet, and you're letting him know every day of his life that it's not normal and it's not okay. It's not how you are (social) and therefore he's an incomplete person. I agree that you can't "read him" - because you only read one kind of story, which is the story of your personality and teen years. You are unwilling to read someone differently, to see someone with a different personality as being whole and fine.
If anything is making him depressed, the number one thing is your behavior. You're telling him also that he cannot survive without you, that he cannot care for himself and make any decisions about how he's feeling without telling you every detail. You're driving him away from you, and I know that's not what you want.
Before you take him to a counselor, please take yourself. I think there's a great truth in your statement that "he is calm... and I am the opposite." Maybe his calmness isn't the problem - maybe your inability to be calm, your anxiousness, is more of a problem. The good news is, this can be treated successfully and you're starting well before he's further into his teens and ready to push you away and keep secrets because you can't handle even the small things.
Please love your son enough to let him be who he is. Please love yourself enough to get help. And as a bonus, your counselor can listen to your descriptions of your son and decide if he's showing obvious signs of depression - so you'll have another opinion (a neutral one) to help you through the teen years. But from what you're saying, there is no way that taking your child to a counselor is going to do anything but backfire right now. BTW most pediatricians screen for depression at the child's annual physical.You can mention it ahead of time to the doctor, but then you MUST leave the room and let your child spend time with the physician alone, partly because of his age and partly because you are way too anxious right now.