you adding live rock 14 days ago and this happening doesn't add up. I can think of 3 things
1. the rock was exposed to extended environmental change like air exposure, cold, heat
2. your dry rock had lots of organic matter decaying after it got wet
3. you had contamination in your tank such as copper medication or antibiotics (furan, general cure, etc) that killed the rock
those 2 things would make the live rock very dead and the result would be exactly what you have experienced here.
the bottle stuff is live bacteria and it will take a bit to establish itself on surfaces and it grows exponentially. You currently have 3 sources of ammonia the fish breathing, leftover food/poop, and whatever last spike killed off your rock like pods, worms, stars etc. my last 2 tanks took 2-3 days to be fully sustaining.
you won't see the numbers for nitrite and nitrate go down until ammonia hits 0.
Can you post some actual numbers for Ammonia and nitrites, its hard to tell what the progress is without the actual number.
you can perform a 25-50% water change tomorrow, that should give you enough time for bacteria to colonize dry rock surface etc.
do you have sand or is it bare bottom?
when doing a water change make sure new water parameters are exactly the same especially specific gravity and temperature of the new water or you will continue to cause die off and spikes.
Do not expose your rock to air when doing the water change to preserve that new biofilm
this might be simple but is the water dechlorinated or RO/DI?
I would also skip a day of feeding, it should help and give biofilter time to catch up.