I will make a review and give some suggestions, comparing it to the closest subclasses currently available to the bard: the College of Valor and the College of Swords.
All three grant control of the medium armor. Valor also awards weapons and martial shields, which is better and offers more options. So it's good.
All three also offer an ability that adds additional damage to attacks. Of the three, you are the only one to use a timer "once per short rest", the other two use Bardic Inspiration dice. Your balance in damages directly. For consistency, I would also ask you to add additional damage of thunder and / or lightning with Bardic Inspiration. This seems to be a bit more related to the Bard theme.
Since the other two have extra capacity (the option to reinforce the air conditioner with Inspiration and a combat style, respectively), adding a spell and a known spell seems to go well. It could even be a little weak at this level.
The three subclasses grant Extra Attack at this level. Nothing to see here, move on.
This ability makes considerable damage guaranteed, and seems to have no restrictions at all. You can potentially use it at each turn while you are in melee (which you belong to), which makes it very powerful compared to the level 14 capabilities of the other two subclasses.
It is likely to cause a lot more damage than the Valor Bard's Battle Magic ability (which uses bonus actions instead of reactions) and almost certainly more than the 1d6 Sword Bard additional damage per hit that does not use Inspiration.
The capacity seems to fit the theme, so I would suggest to cap it. Make it use Inspiration (which makes it a powerful inspiration, but it's probably acceptable at this level), do it once a Short Repos or turn it into a special spell ability (Lightning version of Hellish Rebuke) for her to be exhausted. spell the locations.