How is the trilobite possible?

Resurgence, 

Infertility isn't always a result of non-egg production.  Some women suffer from endometriosis and have a lot of scar tissue on the cervix not allowing implantation of a "normal fetus", some women have cysts in their Fallopian tubes blocking egg transference.  These are all issues that can make a woman infertile then comes the super black goo sperm that can implant and do what it wants.

Well Shaw's case is either her Fallopian tubes are blocked or her ovaries do not produce eggs which she hints at when she says she cannot make life, some might argue that it could go either way but she would most likely know that she would still be making life if she used a surrogate.

Since we don't really know exactly how trilobites are conceived, it's impossible to determine if Shaw's infertility has anything to do with it or not.

actually S.M. it does because her body began to gestate the trilobite similar to a fetus because it even has an umbilical cord.

Well, the black goo seems to be able to do a lot of things but it also seems to pick up traits from the host. Perhaps it's because Shaw is a woman that we get another egglayer (the trilobite)?

"actually S.M. it does because her body began to gestate the trilobite similar to a fetus because it even has an umbilical cord."

Not sure what that has to do with Shaw being infertile.

Couldn't it just be a straight-up parasite implantation? Y'know, like any facehugger would do, except this time it was slightly more of a . . typical sexual transmission what done the trick.

Based on the end result that's quite likely.  An Alien is marrying what the hugger implants and the host.  With the trilobite it likely doesn't need Shaw's genetic material at all - just some place warm to gestate.