How much of a problem is this for me?

To some extent the answer depends on your class and age, but being lactose intolerant in Medieval Europe would not be a major problem in itself. And, you wouldn't be alone either.

First thing to keep in mind is that during Lent animal products like milk would have been forbidden anyway.

Second, remember that this is the era before modern refrigeration, and not everyone could go straight to the cow to get fresh milk.

Rich adults would have been feasting on a shit-ton of meat on permitted days. They had dairy-based treats like cream, but the star of the table was meat.

Lower class adults ate grain and legumes with seasonable fruits and vegetables thrown in. If you owned a cow, goat or sheep then diary might be more important. This is especially true of cheese, which, even if you couldn't eat it, you might be able to get to market before it spoiled, or put down for the winter.

Goats would have been a really great asset not only because they may be easier to maintain than cows, but also because their milk contains a fraction of cow milk's lactose. So you would most likely have been able to drink it without experiencing any discomfort.

Children rich and poor alike would have been weaned on a really gross milk mixture until age 7, after which they moved on to adult food.

For a recreation of medieval dining across classes and events, see this.

What is thought to be the reason for my symptoms?

Unfortunately, I wasn't able to find an answer for this. Hopefully someone more knowledgable can answer.