Cannot insert row into table after creating a trigger
The IF statement should only check the column that is being inserted for 'SI', see revised code.

DELIMITER $$
CREATE TRIGGER aio_mtltp2016 AFTER INSERT ON master_table_linfomastp2016
BEGIN
        IF New.IMHQ_solicitado = 'SI'
        THEN 
        INSERT INTO imhq (ID_CASO,Tipo_de_estudio,Año,Codigo_interno,Iniciales_Px,Sexo,Edad)
        VALUES (NEW.ID_CASO, NEW.Tipo_de_estudio, NEW.Año, NEW.Codigo_Interno, NEW.Iniciales_Px, NEW.Sexo, NEW.Edad);
        END IF;
END;$$
DELIMITER ;