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Lactalbumin is a milk protein, so this would include all milk products and foods containing milk or milk products.
In addition, you need to check labels of pre-made foods you buy (such as bread) for the addition of milk products or milk proteins. Look for these ingredients on the label:
---casein or sodium caseinate,
---lactose (milk sugar)
Lactose intolerance would be a bit different than a true milk allergy. Lactose intolerance would give you the digestive discomfort; whereas a milk allergy may give you a more systemic (whole body) allergic response (examples would be wheezing, skin rashes, headache) as well.
You may have both. People who have food allergies many times will have several.