Do you want to fill a H or do you want to look like a full perky H?
If you want to look like it, you will probably will fill a HH/J bra. I think 300cc is insufficient to actually make you look like an H. When you’re a 34 band size, it is approximately 150cc per cup size. So you will fill out that 34H bra. However, you will probably look like a very full G, maybe small GG. So, exactly the same as now, just perfectly shaped and very full.xx
Tell your ps exactly what you want hun, don’t hesitate to show him pictures of what you want. That is more accurate then just going with cup size.xx