Take a look at Mindfulness Meditation (MN10). This is one of the key meditation suttas. MN10 breaks down meditation as a progression of 16 steps, grouped in four tetrads. The first tetrad is the body tetrad. Your current practice is breath awareness, so you are already doing part of the body tetrad. The following should be familiar to you:
Just mindful, they breathe in. Mindful, they breathe out
Notice that you're not forcing anything. You are simply being aware. This is very important. Just be aware without grasping or rejecting. In particular, do not "choke your thoughts". Instead, invite the mind towards an awareness of and engagement with the steps of the sutta. Following the steps, we eventually see:
They practice breathing in experiencing the whole body. They practice breathing out experiencing the whole body
And so the sutta proceeds through feeling and thence to mind, etc.
Don't skip ahead, especially if your concern is agitation of mind. Although awareness of mind is a tetrad, it's later, after awareness of feeling. First take care of the stuff that makes sense and is doable. For example, you could spend years doing just the first tetrad. I did. Eventually, your own insight will prompt you to the next step when you are ready. It's not a race to be won. It's more like tending a garden--you can't rush this.
If your current awareness of body stops and skips, be aware of the body in the context of your breath. The breath is already smooth from the prior step, so a gentle consideration of the body while breathing will naturally become smooth. In other words, maintain the breath connection (aware of in/out/heavy/light) as your awareness touches the body.
When agitated, we breathe quickly, sometimes 6 or more times a minute. As meditation deepens, you will find that breathing slows on its own and everything settles. Perhaps you may find yourself breathing 3 times a minute. Or even 2. Effortlessly. As the breath calms, so does everything.