Shia perspective: (as you added Shiism tag, it demonstrates you are looking for Shi’I answer(s))
As much as I researched, wearing common sport short in normal way (for men) doesn’t seem to be haram (forbidden) in a common situation (e.g. wearing usual sport short in soccer). But AFAIK there seems to be sin as an impermissible practice in wearing very short/tight Short which lead to sin …
E.g. as a relatively a related issue, it has asked regarding the ruling of wearing specific clothes of the sports such as wrestling/weight-lifting and so on, the answer of Ayatullah Khamenei as a famous Shi’a scholar/Marja’al-Taqlid is that:
حضرت آیة الله خامنه ای(مدظله): اگر ترویج آن باعث گناه و بی بند و باری
باشد جایز نیست.
It is not permissible if its promotion would be led in sin and
Consequently, the following Fatwa of Ayatollah Khamenei can be deemed as a general formula to recognize similar issues. (So, I assume, although the clothes of wrestling/weight-lifting seem to be worse than soccer, you'd better try not to wear short/tight short in order to prevent sin (although what I perceived of your text, doesn't look haram)
And Allah knows best.