I'm no doctor but was taught in school that there was a possibility for females to reproduce without men.

I have to register a healthy dose of scepticism as to the accuracy of that teaching, well-intentioned though it might have been at the time.

To date it's not possible. Some less complicated organisms (frogs, for example) have had their eggs "tricked" into dividing without being fertilized, but no human ova to my knowledge (sub-encyclopedic, I confess).

Theoretically it's not impossible but only in the sense that it's impossible to disprove anything, "really." The whole cloning scientific community is working on figuring out how to do it; Dolly-the-sheep was a breakthrough but needed vast technical support at every step.

No one knows what the product of such a process would be, of course; any of so many things could go awry along the way...and from there we slip back into the realm of speculative fiction, where the idea has been dealt with at length in the past and where it must remain for a while longer.