You should talk to your doctor about what your having HPV might mean for your baby.
"If a pregnant woman has ever had genital warts, she should tell her clinician. A clinician can remove warts before the birth to keep them from bleeding during delivery. A cesarean section may be needed if warts are likely to bleed heavily.
Very rarely, women transmit genital warts to the fetus during vaginal delivery. This can result in serious medical conditions for the newborn, including problems with breathing and severe, sometimes fatal, developmental disabilities."
http://www.plannedparenthood.org/sexual-he
alth/std/genital-warts.htm
Yes, you can give someone warts even if you use a condom.
If your current partner does not trust you and is accusing you of cheating, then he is certainly not worth being with and not raising a baby with anyway. Many people have HPV without any symptoms at all. So you could have had HPV long before you met him. So he has no reason to suggest that you're cheating just based on that.
Don't worry about finding men in the future. Many people have genitals warts. Just be upfront and honest about it. There are plenty of guys out there who also have it, so they certainly should not be worried about being with you.