Yes, you should follow up with a doctor and it would probably be wise to see either a gastroenterologist (digestive disease specialist) or a hepatologist (liver disease specialist).
ALT and AST are referred to as liver enzymes. An elevation in these enzymes usually suggests a problem with the liver. I don't believe that your numbers are so high that they suggest any immediate danger so I would not panic if I were you. But they are elevated and you should seek expert medical advice. Probably the most common cause of an elevation like yours is fatty liver disease. If that turns out to be the case you may be advised to modify your diet and institute an exercise plan. Weight loss and exercise is the most common approach to fatty liver disease. Are you over weight?
We also see elevation in liver enzymes with viral hepatitis such as hepatitis B and C. Frequently these viral infections are not symptomatic and are often discovered during routine blood work.
Drug toxicity and alcohol abuse can also cause liver enzymes to elevate but since you don't drink you can rule out alcohol.
There are other possibilities but I don't think it makes any sense to try and list them all. I think you should get to a specialist - gastroenterologist or hepatologist and find out what is causing your elevated liver enzymes. Unless you live near a large teaching hospital you may have trouble finding a hepatologist in your area but, if there is one available, I think that would be the best doctor to see. But, if there isn't a hepatologist available then a gastroenterologist familiar with liver disorders would be the next best choice.
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