Breastfeeding is messy!
I had over-active letdown in the beginning, which basically means I was a breastmilk fountain. I would literally squirt milk 3-4 inches straight out once letdown occured. My other breast would leak while she was nursing too.
I strongly suggest investing in nursing pads. Stick it in your bra on the opposite side to catch any leaking. I also tucked burp cloths into my bra under the side she was nursing on to catch the overflow. It got better as Avery got older. I guess my nipples just figured out the proper flow, LOL.
In general, applying firm pressure to the breast while it's leaking can stop it. In the mornings when I'm really full I still have to put a bra on before I nurse so the pressure keeps my other side from leaking. Otherwise, I'd just keep nursing pads on you at all times until things calm down.