Which one do you want to measure? I know of some scales that measure critical thinking, some that measure creativity, but no scales that try to do both in one index.
You ask whether there is any psychological test to measure thinking pattern of school children (age group 13-16).
As you certainly know, Jean Piaget was highly concerned, not with how much one is intelligent (e. g. one's IQ = 120, 130, 140, and so forth), but with one's type or pattern of intelligence, knowing, and thinking (e.g., concrete operational intelligence, formal operational intelligence).
As is obvious, one's quantitative intelligence has nothing to do with one's thinking pattern, just because it is quantitative. In contradistinction, Piaget's developmental tasks (e.g., the number conservation task, the pendulum task) are, above all, concerned with one's thinking pattern, not with how much we are intelligent
In this vein, compared to concrete operational thinking, formal operational thinking represents a better and more developed thinking pattern, form, or structure because it differentiates and integrates more dimensions, perspectives, and the like.
Also, according to Piaget, formal operational thinking tends to exist in adolescents, not in children.
Thus, I would say that Piagetian developmental tasks are the most suitable tasks (tests in your question) to assess one's thinking pattern, form, or structure. As you want to assess such pattern in a age group (13-16-year-olds) composed of adolescents, then you could employ Piagetian developmental tasks that are appropriate to grasp adolescents' thinking pattern. The great majority of these tasks appear in the following book: Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to adolescence. New York. Basic Books. (Original work published in 1955).
In your question, you refer to measure. As I see it, in psychology, it's better to speak of assessment or evaluation instead of measure. To speak of measure in psychology makes us think of a degree or rigor that doesn't exist in psychology, and that exists only in the so called "hard sciences", physics, for instance. Note that in a mental test (e.g., WAIS or WISC), a given score ( 120, for instance) can be got by answering differently to the several items the test/scale contains. Thus, the same score can refer to different mental realities. I know that we, as psychologists, often speak of measure instead of assessment or evaluation. However, if we perform a conceptual, grammatical or philosophical investigation a la Wittgenstein, we may reach the conclusion that rarely, if ever, psychology attains the level of measure. Moreover, a falsity does not become true simply because it is accepted by a great number of people.
The lack of conceptual clarity in most psychological domains partly explains what Paul Meehl called in 1978 (see Journal of Consulting and Clinical Psychology) the "slow progress of soft psychology".
In my answer to your question, I wanted to pay due attention to the concept of thinking pattern, style or structure. As I see it, this concept has more to do with one's type of qualitative intelligence a la Piaget, for example, than one's quantitative intelligence a la Catell, for instance. Also, I am sure that you are fully aware that to ask for adolescents' thinking pattern has more to do with their form, structure, or type of thinking than their quantitative intelligence. This is the main reason that led me to suggest that you may appeal to Piagetian developmental tasks to assess the thinking pattern of your age group.
I hope that I have got your question and that this helps.