The key point to remember here is that everything you eat will make you breathe more deeply. Some foods will make you breathe more than other foods. Plus there is some individual variation in how much people respond do different foods.
With this issue please realize that you will need to eat something to stay alive. As all foods increase your breathing depth [because of the digestive process], your breathing is going to be affected, there is no avoiding it. The strategy is simply when your breathing is poor, and you are having symptoms, eat as little as possible and eat the foods that have least effect on your breathing.
Remember that the problem is to do with your breathing, that is where the most important focus of your recovery should be. It is your shallow breathing practice that is more important than anything else, including diet.
The foods which tend to increase breathing the most are animal proteins, animal fats and refined sugars. This includes chicken, beef and other meats, and milk products. Plant proteins and fats are less harmful. Nuts, beans, berries and other fruits can have strong impact on some individuals breathing.
The rule is to reduce animal protein as much as possible, and observe your breathing after eating. Always reduce your breathing after food to reduce the impact of the food. Once your breathing has been conditioned to maintain a higher CO2 level, you will be less affected by what you eat.
Until then, minimise or stop your meat intake, along with all dairy foods. [Note: Soy milk is very high in protein, and only slightly less harmful than animal milk in breathing terms.]
Another notable food that increases your breathing very strongly is alcohol. If you have symptoms of asthma do not drink alcohol. If you doubt this, simply measure your pause before a few drinks, then measure it afterwards.
Major Rule of Food
If you are not hungry, do not eat. If you do not feel hunger, your body is not ready for food, and will not digest it efficiently. If you are not sure if your are hungry, wait for a while.
During the first week of training your breathing, especially if you have symptoms, follow this rule rigidly. If you do not eat for several days, fine. Wait until you are hungry.
The less you eat, the faster your breathing will improve.