Just to clarify - are you allergic to cow’s milk or lactose intolerant? It’s important to know the difference.
Lactose intolerant means you can no longer digest the lactose in milk. This means you should have problems with ALL milk products regardless of source. However, there are lactase tablets sold that can help you digest dairy IF that is the case.
If, however, you are allergic cow’s milk that is a different problem. It has nothing to do with “enzymes”, the problem is that you are reacting to cow protein. There is no tablet to take to help you with it. “Low” and “no” lactose milk isn’t going to help because in this case it’s not the lactose that is the problem, it is the cow protein.
From what you describe, I suspect it’s a cow allergy, as you state you tolerate goat’s milk.
What that means is no more dairy from COWS. You can drink goat’s milk. You can eat goat cheese. You can eat sheep cheese. That is because goat and sheep milk don’t contain cow proteins. (There’s your answer on cheese). You can not consume yogurt that is made from cow’s milk, including frozen yogurt and things like tziki sauce (that white stuff on gyros sandwhiches).
You are going to have to read labels from now on. In addition to “milk” you have to watch out for words like “whey” and “casein”, which are also derived from cow’s milk and contain the offending proteins. You will have to educate yourself about condiments, some of which contain milk products (such as the above mentioned greek sauce). You will need to avoid cream soups, many or most gravies unless made explicitly without milk, and cheese sauces which are also almost universally made with cow’s milk.
As Jews are particular about mixing dairy with meat, you might want to check out the kosher foods at your local grocery as they are quite explicit about what does and does not contain dairy.
Chocolate is giving you a problem because most chocolate is milk chocolate, meaning there is milk of cow origin in it. That is why it is giving you a problem. You will need to find chocolate that is NOT milk chocolate. For example, if you make hot cocoa from scratch you will need chocolate that doesn’t have milk in it and use goat’s milk instead of cow’s milk to make it.