Well, you should first consult with your doctor to fully understand the severity of your inability to ingest cheese.

First, it's worth knowing that lactose intolerance and a milk allergy are two different things. A milk allergy is a reaction to the proteins in milk (casein or whey), not to lactose. If you have one, you'll want to avoid cheese and all dairy products completely. Allergic reactions can be serious and/or deadly.

For those of you that have true lactose intolerance, there are a few ways you can eat cheese without duress:

1. Choose aged hard cheeses: much of the lactose drains off with the whey, and what's left breaks down as the cheese ages, so cheeses aged over a few months (cheddar, Swiss, aged Gouda, Parmigiano Reggiano) generally have much less lactose than fresh or processed cheeses (think Velveeta). If you're not taking medicine, you may be able to eat an aged parmigiano reggiano without upsetting your stomach.
2. Keep portions small and eat them with a meal. Many people tolerate a little lactose better than a lot.
3. Take medicine: lactase supplements are widely available over the counter. Typically you'll take a pill right before your meal and you'll stand up at the end without consequence.
4. Look for lactose-free cheeses. They're easier to find than they used to be.