Colic/discomfort are very common in the first few months of life, when babies’ tummies are still immature. The amount of milk they drink in proportion to their body weights is enormous! So for most babies, discomfort has nothing to do with an allergy but rather with an immature gut which gets better on its own by 3-4 months of age.
There are exceptions- those with early onset eczema, failure to grow, excessive reflux in addition to discomfort may need to be assessed for a cow’s milk allergy. Remember that small amounts of cow’s milk protein can be transmitted via breast milk, so in selected cases a trial of exclusion of cow’s milk from mom’s diet may be considered. However, the emphasis here is on selected cases after discussion with your healthcare practitioner.
Remember that lactose intolerance is very different to cow’s milk allergy- lactose is the SUGAR in both cow’s milk based products and breast milk….so reducing mum’s dairy intake will do nothing to treat “lactose intolerance” as mon’s milk is lactose-based anyway!