As indicated by you both of you would be cousins and as such such a marriage is prohibited under the Hindu Marriage act as such relationships falls into Sapinda Relationship.
However, you have to see the custom of your society and if such marriages have taken place in your society and the couples are enjoying blissful lives after their marriage knots, you can think of such a marriage. However, you need to take your parents into confidence and in turn your parents should proceed for talks with the family of your fiancé. This should proceed with the cordiality and the relationship is settled amicably.
In that way, your relationship would be smooth in your marriage journey but keeping in mind of such a closed relationship, take the suggestion of your physician who might evaluate DNA and other blood tests to ensure that no complication would arise as a result of such an alliance.