Is it wrong to wear short-sleeved shirts?
Generally it is permissible to wear short/half sleeve shirt or ghallabiyya unless there is some other element of impermissibility, such as the clothing is made of silk, or it is the exclusive dress of the unbelievers (kuffar), etc…
However, the Fuqaha mention that it is prohibitively disliked (makruh tahriman) to offer Salat with rolled-up sleeves, for it is contrary to proper etiquettes (adab) of Salat. If one entered Salat in such a state, then it would be better to un-roll them with minimizing the movements as much as possible.
Allama Ibn Abidin (Allah have mercy on him) states:
“It is Makruh to enter into Salat with the sleeves rolled-up……and to roll-up the sleeves whilst in Salat will invalidate the prayer, for it will be considered to be excessive movement.” (Radd al-Muhtar, 1/ 640)
As for praying in a shirt or Ghallabiyya (jubba) that has short sleeves (and not rolled-up), it would seem that there is nothing wrong in doing so. However, if it is considered to be from the lowly cloths that one is ashamed of wearing in front of respectable people, then it would be Makruh to pray in it.
Imam al-Haskafi (Allah have mercy on him) stated in his Durr al-Mukhtar
“(And it is disliked to pray in lowly clothes) that one wears at home… if one has others, otherwise it is not disliked.” (See: Radd al-Muhtar ala al-Durr al-Mukhtar, 1/640)
And Allah knows best
[Mufti] Muhammad ibn Adam
Darul Iftaa
Leicester , UK