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. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Whoever suckles the milk of a woman five times or more in a period of two years, becomes her son/daughter by suckling relationship. So if your cousin suckled your grandmother in the manner you mentioned then he had become her suckling son. The ruling that applies to suckling is the saying of the Prophet : "What is prohibited by reason of family lineage is also prohibited by suckling relationship." [Al-Bukhari and An-Nasaa'ee]
If you mean by grandmother, your mother's or your father's mother, then your cousin is your suckling uncle, so he is a Mahram (non-marriageable relative) to you and to your sisters. However, his brothers are not Mahaarim for you, therefore you can marry them.
Allaah knows best.