It's hard to know what your biology teacher meant, so it's hard to know how to answer. Perhaps the best thing to do is just give a quick summary of the current state of theories in fundamental physics.
First, a general note: a theory can be "wrong" in a strict sense and still be very useful. Newtonian mechanics is "wrong", strictly speaking, but it is still used extensively, because it's a good enough approximation for many purposes. I'm assuming that by "wrong", your biology teacher did not mean the theory is wrong the way that, say, "flat Earth theory" is wrong, but only the way that Newtonian mechanics is "wrong".
That said, here's a quick overview of the current state of physical theories:
(1) For situations in which everything moves very slowly compared to the speed of light, and in which gravity is not too strong, Newtonian mechanics is a good approximation and is still extensively used, as noted above.
(2) For situations in which things move fast enough compared to the speed of light, but there is no gravity (or at least negligible gravity), Special Relativity is a better approximation than Newtonian mechanics and is also used extensively. However, Special Relativity cannot handle gravity; see next item.
(3) For situations in which things move fast enough compared to the speed of light, and gravity is not negligible, General Relativity is used. Also, for situations in which gravity is strong enough, General Relativity has to be used even if nothing is moving fast compared to the speed of light; for example, we have to use General Relativity to study neutron stars, because their gravity is strong enough that Newtonian theory is not a good approximation. For all situations in which quantum effects are negligible, General Relativity is the best current theory we have.
(4) For situations in which quantum effects are not negligible, we know how to add quantum mechanics to the theories in cases #1 and #2 above; this results in ordinary (non-relativistic) quantum mechanics, and quantum field theory, respectively. For all situations that these cases cover (i.e., situations where quantum effects are not negligible, but gravity can be neglected), quantum mechanics and quantum field theory are the best current theories we have. For example, the Standard Model of Particle Physics is based on quantum field theory, which includes Special Relativity.
(5) We do not have a good current theory that combines quantum field theory with General Relativity; one of the primary efforts in theoretical physics today is to come up with a theory of quantum gravity that unifies quantum field theory with General Relativity. String theory is one candidate for a theory of quantum gravity; it gets the most press, but is not the only candidate.
If you need more information, it would help to be more specific about exactly what your teacher said.