ex nail technician here, I too was super worried about my ails doing just that, (what has happened to you) and I use to teach my students about the effects chemo had on the nails, I'm do sorry you have experienced this,
my go to product is cuticle oil, try if you can pending on how sore your fingers are, to drop a drop of cuticle oil on the cuticles of each nail if not just above the cuticle, and massage in very gently, this will help promote the growth in the matrix that lye's under the skin and just above the cuticle, this is where our nails grow from, try and keep nails short so they do not catch on anything, if your nails are discoloured and you can put polish on them to hide the discolouration then do so, if infected, then I would recommend not, as then you can keep an eye on how the infection is healing, nails will grow back in around 6 months time, try also adding a nail strengthen to add some protection to the nail plate for extra strength at this time.
good luck with getting through this chemo journey, I feel your pain.