Overwhelmed
When you cannot stand to be touched one more time
Being touched out is a specific, physical experience, not the same thing as general stress. It is real, and it's common enough that parents have a name for it.
This is physical as much as emotional, even though it can feel confusing
Hours of being climbed on, nursed, carried, and grabbed at can build a genuine physical urge to pull away from any more touch, even a loving one, even from your own child. This is a common response to hours of nonstop contact and noise, not a measure of how much you love them.
Flinching away from touch does not mean you are touch-averse, or failing at anything
Feeling a strong aversion to contact in this specific, saturated moment does not mean you dislike physical affection generally, and on its own, it is not usually a sign of some deeper problem. It is a passing state, not a permanent trait or a character flaw. If it feels this way most of the time, or comes with numbness, dread or feeling far away from your child, that is worth bringing to your doctor.
Noise usually compounds it, it is rarely touch alone
Constant sound, chatter, crying, toys, screaming, is often happening at the same time as the physical contact, and both channels being saturated together is what creates the urgent need for quiet space, not simply less touching in isolation.
Needing a few minutes of no physical contact from anyone, including people you love, is a legitimate need, not a failure of patience or affection.