Forget the inch per gallon rule, it is outdated and doesn't take many things, such as bioload and territorial behaviours, into account. You can apply it to neon tetras, I suppose, but that's about it. For instance, by the inch rule you could fit a ten-inch goldfish in a ten gallon tank (you couldn't), yet only have two or three kuhli loaches (when you can actually have 5).
However, there is a bit of a problem with your stocking.
"3 neons, 3 rummy noses, 2 golden barbs, 2 harlequins, one guppy and a teeny tiny nano shrimp".
All of the fish except your guppy are schooling fish and need groups of 6 or more to be content. In smaller groups, they will be more stressed and therefore be more likely to get six. To properly provide a school for each of your fish, you are looking at a good 100+ litres.
I strongly recommend rehoming 4 of those schooling groups and just focussing on one - either the rasboras (assuming they are harlequins, not scissortails or something) or the neons would be my choice for a 45 litre tank. The others are larger, and the rummies are more delicate. 6 neons and 3 guppies (yes, they like groups too!) would stock you nicely. :)
And to confirm the answer to your original question, your betta is indeed a red veiltail. :)