I am allergic to chicken, pork, beef, clam, egg, soy, barley, oat, cashew, brazil nut, and english walnut. Could I have a protein intolerance?

What kind of allergy. Prick, blood tests not very accurate re: food allergies. Neg tests exclude an immune reaction (true allergy), but pos tests have less value. Best test is a double-blind food challenge (neither tester nor pt know which is which, until code is cracked at end of test); cumbersome.This excludes about 90% of "allergies". Other blood tests can be used, not "live-cell"-bogus, no "applied kinesiology".
Please see allergist. It would be very uncommon to be truly allergic to all of these foods. See an allergist for further diagnosis and management. An oral food challenge is the gold standard for diagnosing food allergies.
Protein intoleerance. Protein intolerance is an inability to metabolize or digest certain proteins. It is not an allergy. Thus, having allergic reactions to the multiple substances you mention would have nothing to do with protein intolerance. Allergies usually cause itching and rashes, sometimes wheezing. Protein intolerance tends to cause malabsorption of food, weight loss, nausea, weakness, etc.
Q for Allergists, GI. Thank you for providing additional information in the comments to prior answers. I will share this with some additional specialists and subspecialists on our site.
No. First, you can't be intolerant of proteins in general, only to some here & there. Second, i find it hard to believe that you are truly allergic to all of these things. An allergy is a specific immune reaction (e.g. Difficulty breathing, swelling, rash, & other well-defined symptoms). If, for example, you just get vomitting, mild stomach ache, or watery diarrhea, then you are intolerant only.