Typically sperm will die when exposed to air for a few seonds although there is always exceptions to to rule. I do not know of this happening or to be true so I wouldn't worry about sperm leaking through your gym shorts and into your GF.
Be safe and use common sense and I think you should be alright in the future.
Information on this site is provided for informational purposes only.
It is not meant to substitute for medical advice provided by your physician or other medical professional.
If you have or suspect that you have a medical problem, promptly contact your physician or health care provider.