is my partner the father?

i am 33wks pregnant. i conceived on the 11th of march. i had unprotected sex with my partner around the 2-5 of march, but 3 or 4 days later had sex with another man. he did not come inside me although we didnt use protection. this man has also said he hasnt had very good sperm count. me and this man began seeing each other but he did not come inside me until after the 11th (after id conceived). my partner is the only 1 to have come inside me before i conceived (7-10 days earlier). is he the father?