Amina Inloes, Amina Inloes is originally from the US and has a PhD in Islamic Studies from the University of Exeter on Shi'a hadith. She is the program leader for the MA Islamic Studies program at the... Answered 1 year ago

A cousin is not mahram unless you are married to them or is a secondary reason why you are mahram (such as being milk siblings). However you do not need a mahram to go to hajj.  This is just a legal requirement for the visa from Saudi and is not required in Shi'i fiqh.

I hope you are able to perform the hajj successfully, God willing!