We are not the owners of our body, blood etc. Allah The Most Gracious is the owner of all this. We cannot donate what we cannot own.
If there is a danger to the life of somebody and giving blood can save life, then donating blood is allowed, as in times of need, what is prohibited also becomes allowed (Mubah). It should also be kept in mind that the person who donates blood should not suffer any harm from it.
It is better if you take the advice of your elders and parents in this regard.
And Allah The Most Merciful and The Most Beneficent knows best.
Mufti Syed Ziauddin Naqshbandi Qadri
[Professor, Islamic Law, Jamia Nizamia,
Founder-Director Abul Hasanaat Islamic Research Center]