Can my cousin fix my papers if I came to the US with visitor visa?

It depends on the state where you live. USCIS will recognize a marriage if it is: a) a bona fide marriage (i.e., with genuine intent to create a family); b) legal under the laws of the jurisdiction where it was solemnized; and c) the only marriage of each party (even if the solemnizing jurisdiction allows marriage to two or more spouses) For example, New York has no prohibition against marriage of first cousins and recognizes same-sex marriage. So, if you live and marry your cousin in New York, your marriage will be valid for the immigration law purposes (if it is a true marriage and neither of you has other spouses). Some states prohibit cousins' marriage but will recognize it if the marriage was solemnized in another state. For example, you cannot marry your cousin in Illinois, but, if you married her in California and later moved to Illinois, Illinois will not say that you are not legally married (but be careful: if you lived in California at the time of the marriage, it is OK, but, if you were actually a resident of Illinois and moved to California for a brief time just to get married, Illinois can consider your marriage illegal).

If you were married in a jurisdiction that allows such relations, she probably will be able to sponsor you. I suggest discussing your case with an attorney as this could be an issue that needs to be adequately explained to the government adjudicator.