The father is the second guy. Once the baby is born (so, any time since October), you should go with him and the baby to the doctor and do a DNA test, not because there is any doubt (this baby would have been conceived around January 14) but because you want the dad to be in the baby's medical record for legal reasons. If ever you were to need to file for child support, you could point to the fact that a DNA test was done and the record has been in your child's file all this time.
Given that it is the second guy, do the DNA test and get it all confirmed officially so you'll never have a legal fight over this later.