If I conceived April 7th 2013, but had sex on march 30th 2013 does that add up?

It can. Conception isn't instant. It takes a while for the sperm to travel, meet the egg, penetrate the egg, and for the egg to travel and implant in the uterus. It's not instant.

Having said that, why the concern? Is there a question about paternity here?

Yes there is and I am worried, I had sex with the other person on the 1st or 2nd of April 2013

Usually doctors track conception based on your last period. It's not exact. Even an ultrasound can't tell you when you conceived. Why? There's no way to know when you ovulated unless you've been tracking ovulation daily with basal temperature for at least 6 months. Conception dates can be off 2 weeks either way, with equals to a month.

You're in a tough spot, a waiting game, and it won't be easy. You really only have one choice here, and that's a DNA test after the baby is born. The dates you had sex are too close together to accurately tell you who the father is.

I'm sorry. I wish I could tell you who the daddy is, but I can't. No one can. You'll have to wait and see.

I wish you all the best.