我想你需要下面的陈述
https://www.db-fiddle.com/f/jbdzxwpwkyichsbl1ib2rj/2

select constraint_name
  from information_schema.table_constraints
 where table_name = 'mytable'
   and table_schema = 'myschema'
   and constraint_name = 'PRIMARY';

或以下https://www.db-fiddle.com/f/jbdzxwpwkyichsbl1ib2rj/3

SELECT EXISTS(
  SELECT 1
  FROM information_schema.columns
  WHERE 
     table_name='messages'
     and column_key = 'PRI'
) As HasPrimaryKey;

SELECT * FROM INFORMATION_SCHEMA.COLUMNS
WHERE table_schema = schema()
AND column_key = 'PRI'
AND table_name = 'my_table_name'
AND column_name = 'column_name';