Yes, you can have all these fishes in 10 Gallons. But my only concern is cory catfish, other two varieties and numbers are pretty fine. If cory catfish is of smaller size it is fine.
Dwarf gowrami can grow little bigger, but not a problem as you have only 1. But still you have some doubts, you can go ahead adding 4 more to your neon school, or zebra danio's or minnow's. Tiger barb can be also added. But get any of these fish only 4 or less as u have a 10 gallon tank already with 7 fishes - 3 cory + 4 neon.
Dwarf gowrami can grow little bigger, but not a problem as you have only 1. But still you have some doubts, you can go ahead adding 4 more to your neon school, or zebra danio's or minnow's. Tiger barb can be also added. But get any of these fish only 4 or less as u have a 10 gallon tank already with 7 fishes - 3 cory + 4 neon.