Is there any risk of illness from eating shellfish?

Yes. Shellfish is among the most common food allergens. Do not eat shellfish if you are allergic to it. Cooking, freezing, or refrigeration of shellfish will not alter the outcome. 
 
Food-borne outbreaks of the Norwalk virus, which causes gastroenteritis, are often associated with consumption of raw shellfish. So are outbreaks involving Vibrio parahaemolyticus, a bacteria that causes mild stomach illness in healthy people and serious illness in the elderly or those with weak immune systems. Vibrio vulnificus, a bacteria common to raw  oysters, also can cause gastrointestinal illness, as well as more serious illness. It is associated with high mortality rates among those with a weakened immune systems or poor liver function. 
 
Shellfish also can harbor intestinal parasites, though parasitic infections occur less frequently than bacterial and viral infections.
 
Another concern is spoilage, which doesn't cause illness but can make food taste, smell, and look bad. It  occurs quickly in shucked shellfish that aren’t properly refrigerated or frozen. Do not eat shellfish if it  has an “off “odor or flavor, or if it has undergone a color change. 
 
The good news is that proper cooking rids seafood of all microbial and parasitic infections, save for microbial toxic metabolites from bacteria such as staphylococcus. These can be introduced to shellfish as a result of poor handling during harvesting, processing, or preparation. Poor handling also can introduce the virus Hepatitis A to shellfish.
 
Source(s):
FDA "The Norwalk virus family"
Redorbit.com "Clams Added to Pacific Northwest Shellfish Warning"
Charkbait.com "The Fishermen's Journal: Fish Parasites"
Sixwise.com "Shellfish: Are They Good for You or Not?"