When I started meditation it was also a major problem for me.
Just as you described, when you are unconsiously controlling your breath while trying not to, you either breath too much or too little. The sensation is really unpleasant as, in addiation to the bad breathing, it feels like you are not doing the meditation right.
This is a good thing to realize, because you will know that you are controlling your breath as soon as these symptoms arise.
So one of the reaction you may have is trying to force not controlling your breath, and to make all kind of mental effort. This is not a good solution, because it will create tension and hinder your concentration even more.
What tend to work for me is the exact opposite reaction: just relax, take a step back
Think that this meditation is a skill that needs a lot of time and practice, and that you are not supposed to do everything perfectely when you are beginning.
Maybe take a little break from the breathing, switch your object of concentration to the sounds in the room, or the sensation in your feets, while your breath naturaly comes back to it's own pace. Then, rather than trying on the breath as one single entity, you may try to break it down in several parts: experience what sensations arise on the inspiration, the expiration, what you feel in your nose, in the abdomen, what is the quality of air in the room, it is warm, cold, etc.
Rather than focusing on controlling or not controlling the breath, or trying to experience the pace of the flow of air, which can be very challenging at first, you might try to focus on other sensation that involve the breath, like those that I described above, which I believe are easier to meditate on at this stage.
As you progress, you will find it easier not to controll the breath, remember that it is a skill that you do not need to master right now. It is really easy to make wrong jugement about yourself because you feel like you are not progressing quickly enough, or because you feel like your meditation session is not working as intented.
I think what really matters at first, is sitting through all of this, no matter what happens. The key is to relax and let the problems arise, notice them and let them disappear by themselves. No forcing, no jugement.
Good luck :)