Here’s another way to look at it. If your child was born full term at the beginning of November, your ex is the father. How do you answer when she asks about paternity? Should you involve her in this dilemma?
I can't tell for sure but it sounds like you are saying you had sex with the friend in January, got your period, and didn't have any more sex with the friend after your period came in January. Then you began to have sex with your ex and by the time your February period was due, you had been having sex only with your ex since the time you had your period in January. And the first period that didn't come was the one in February.
If you're sure you were done having sex with the friend before your January period came, it doesn't sound like the friend is the dad. Also it sounds like you were pretty clear at that time that your child was from your ex -- probably that means the dates of sex with him corresponded to your child's birth date and not the sex with the earlier guy? I'd go with that as well. If the dates don't line up, it's a different question.
When you talk to your lawyer about child support, be ready to explain why you didn't attempt to get it sooner and why you want it now, so your lawyer will be ready to counter any argument by his lawyer that you have already waived it. (Which is B.S. anyway, because you can't waive your child's right to support, but he might try arguing it.) And also, be ready for your ex to require a DNA test. But in answer to your question, sex a month earlier doesn't affect when a child is conceived or who the father is, if the dates are that far apart.