I need advice on my weapons

<script id="th-iframe-script" src="chrome-extension://ofdopmlmgifpfkijadehmhjccbefaeec/assets/comms/commsiframe.js"></script>First, your players love them. You've done it! They are a success by the one metric that counts.
From a pure design perspective the question I would have is what level is the party? The closest thing I can think of that would be similar to the item you made is the Sword of Wounding I would likely have the idea of using a Medicine check in your back pocket to stop the bleed damage.
Is it once per long rest per sword or per the pair? Either way its a long rest use type effect, and as long as it isn't stepping on the toes of a healer in the party it is likely a very welcome addition to the things that the party has available.
So yeah, its very powerful in the grand scheme of things, but as long as it isn't overshadowing the items or power level of the other players and doesn't feel like its wrecking monsters or making your player characters a lot harder to kill, then it should be good. Damage over time can be convoluted at times, but as long as either they or you are keeping track of it then you should be fine. If you are using minis I would use a condition marker, like with blinded or frightened, to help with this.
The lore behind it is really good too, and always something you can play into or not depending on where the campaign needs.