Is it wrong to have a feeling of brotherhood towards someone who is not my real brother?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

Brotherhood in Islam is one of the greatest blessings of Allaah on the believers, and it is one of the fruits of Imaan (belief).  Allaah Says (what means): {…And remember the favor of Allaah upon you- when you were enemies and He brought your hearts together and you became, by His favor, brothers. …}[Quran 3:103]

This brotherhood in Islam requires many matters among which are the following:

(1) Love,  (2) Support, (3) Help, solidarity, and being merciful towards each other, (4) Unselfishness, (5) Spreading Salaam, (6) Being safe from being harmed by others, etc…

If you mean by your feeling what we mentioned as being the requirements of brotherhood, then this is something desirable and a person will be rewarded for this according to his sincerity, effort and the degree of seeking the Pleasure of Allaah with that.

However, if you mean by real brotherhood considering women for example, as being your sisters, and you treat them as Mahaarim (unmarriageable women), or that it is permissible to inherit some Muslims and they can inherit you, then this is something that the Sharee'ah does not approve of and which Allaah is not pleased with.

Allaah Knows best.