It is not possible to have both short-sightedness (myopia) and long-sightedness (hypermetropia). It is more likely that you have a combination of myopia and presbyopia (old-sight, or the inability to read near objects). This is a situation that is commonly confused by many of my patients.
Myopic patients have an eye-ball that is longer than the refractive state of the eye, and hence require a negative / concave lens in order to see clearly for distance.
Hypermetropic patients have an eye-ball that is shorter than the refractive state of the eye, and hence require a positive / convex lens in order to see clearly for distance, however many young patients are able to "accommodate" (or increase the positive power of their internal lens) in order to overcome this refractive error if they are less than +3/+4 hyperopia.
Presbyopia is a condition where the internal lens of the eye has lost its ability to accommodate / increase its convexity in order to allow you to read near text / see near objects. Presbyopia occurs to ALL patients, both myopic and hypermetropic.
However hypermetropic patients are at an added disadvantage when they become presbyopic. They become symptomatic at a much earlier stage than myopic patients, and will need spectacle correction for distance and near. Myopic patients become symptomatic for presbyopia much later, as they continue to wear their spectacles for distance, and are able to read for near either by removing their spectacles (near-sightedness), or pushing their spectacles further down along their noses.
Hope this is helpful in clarifying your situation. For scenarios specific to your situation, you should consult your ophthalmologist!