You can use mindfulness of the actual sensations of the breath as your "anchor" meditation object but when there is a distraction then the distraction itself, as it is, becomes the meditation object until it falls or it is appropriate to go back to the anchor object that is usually the breath (although it could be any aspect of experience depending on who is teaching or what the technique is).
The distractions are not judged (if they are then that very judging or partiality is a distraction that can be the next object focused on, as it is, in the present moment).
We have all kinds of emotional feelings like anger, impartiality, sadness, disgust, disliking, liking, euphoria, delight, happiness, partiality and so on
We also have perceptions, thoughts and more or less solid opinions.
We have physical sensations that can often give us a clue to how we're feeling. Like tension in the neck and shoulders or a wonderful warm fuzzy feeling in the heart or it can just be an itch, pain, warmth, cold, shock, ache and so on.
We have all kinds of emotional feelings like anger, impartiality, sadness, disgust, disliking, liking, euphoria, delight, happiness and partiality.
These are examples of the kinds of experiences that arise through the senses and the mind all the time, if wee notice them or if we don't notice them.
When we really get into this kind of meditation, we will see how one thing leads to another and we start seeing more and more subtly in our own experience. We will often see how subtly partial we are with every experience we focus on. The idea is to have equanimity or full impartiality at even the most subtle level. This kind of meditation with morality and concentration* will slowly show us how to let go and accept reality as it is so we can...
...understand how to live
...be ready when we get sick
...be ready and in harmony with death
*Some techniques have the concentration part built into the meditation such as the Mahasi Technique.
There are many techniques but all I know how to tell people about adequately is the one I do myself -- two links to the full on step by step Mahasi technique (insight meditation):