Right Im going to just tell it as it is, a few people have tip toed around the subject but the fish you have chosen need to be kept in greater numbers than they are at present. In my opinion your stocking should be -
3 x Platy (the baby will grow so needs to be counted, do you have 2 males or 2 female or 1 male 1 female?)
6 x Black Phantom Tetra OR 6x Black Widow Tetra
8 x Neon Tetra
6 x Cory Catfish (all the same species as the 2 you have) or 6 x Dwarf Chain Loach
Apart from the platies all your fish need to be in groups of at least 6 how ever if you went for 6 of everything you would be over stocked. While the black phantoms and the black widows look similar they are quite different in behavior with one being quite nippy (the widows) and the other pretty calm - they will school together but it is not really ideal and you would be better off in the long run just sticking to the one type. Apart from the behavior the only real difference is one has 1 black stripe and the other has 2 personally I would choose the phantoms as like I say they are less prone to nipping like the widows (which is a real consideration if you want a betta). Equally the loaches and the cory cats need to be in groups of 6 again to cut down the level of stress on the individual fish - in the wild the tetras, loaches and cories are found in shoals/schools of hundreds so when people say 6 minimum it really is a minimum number personally I usually stick to one type of schooling fish to maximize natural behavior and also to make them more predictable with levels of stress and signs of a hierarchy developing. So like I say choose between the loaches and the catfish - if you go with the catfish make sure you get the same species of catfish like if you have 2 bronze catfish get more bronze ones or if you have panda ones get all panda ones etc etc its the same principle I was saying with the tetras, they will shoal with each other but its not ideal by any means.
If you were to go with my suggestions that would leave you with a slot open for a feature fish - like a betta but they can be problematic with tank mates but your other options are things like dwarf gourami or honey gourami or bolivian rams (not blue rams though as they have quite specialist needs) other dwarf cichlids like checkerboard cichlids or laetacaras would work as well.
Or if you wanted to up all your fish to the correct numbers (ie at least 6 of all the tetras, loaches and cories) consider a bigger tank something like a 30g would make that work but I would go for a 40g as that way you would be able to consider some different species of fish to go with the ones you have at present rather than just add more of the same species.
Sorry to be so harsh but shoaling fish in those low numbers will eventually end up in such high levels of stress it could only take a small trigger to set some serious problems in the tank. Those small problems could be a slight fluctuation in water temperature at a water change, someone banging on the glass, one fish becoming dominant and adding more stress to the others (a strong possibility between the two lots of disk tetras) Like I say sorry to be harsh but just trying to help and its often better just to get straight to the point than try and coax someone into a new way of thinking.
Wills
The siamese fighting fish, i had one, beautiful it was, a male, was very aggresive towards the other fish, several neons disappeared too 
