I have had tight feeling in chest/dizziness/loss of feeling in hands/loss of balance for last couple weeks even without really exerting myself, what is happening?

Anxiety?: At your age and in the absence of risk factors (hypertension, diabetes etc), your symptoms are compatible with hyperventilation related to anxiety. If you are under undue amount of stress, need to find ways to reduce it. In the meanwhile, your doctor may prescribe something to reduce your anxiety and obtain some tests to make sure that your health is ok otherwise.

? anxiety: The collection of symptoms you describe are all common in anxiety/panic attacks. What I can't tell from your description is whether these symptoms are coming & going or constant. Intermittent symptoms would be more fitting with anxiety/panic. A review in person with your Dr would help to clarify as they could also perform a physical exam to reassure us there was no features of neurological issues.