The longer an object, the greater the surface to volume ratio. That means an elongated object can gain or lose heat more easily than a cube of the same volume, since heat exchange is directly proportional to surface area. As a result, people who have been living in an area for a long time tend to evolve different heights to suit the local climate. People from warm areas tend to be tall, with long arms and legs, and a slender build. People from cold climates tend to be shorter, with shorter arms and legs, and a rounded torso, in addition to having more body and facial hair since these features reduce heat loss to the environment.
That means genes do determine height. However, nutrition also plays a part. We do not know what your diet is really like so we cannot tell whether you have a good diet or a bad one. People with a poor diet will definitely not reach their maximum potential height. People who have insufficient calcium in their diet may suffer from rickets, which can result in deformed or broken bones, even death. It is not unusual to see severely malnourished children being a fraction of their expected height based on their age. After all, muscles and bones need nutrients to grow. Genes are instructions, and they cannot magically order proteins and other nutrients to appear. Think of genes as the blueprint for a building and food as the building material. Even if the blueprint specifies that the building should be 100 stories, no one can build it to that height if there is not enough building material to finish the job.