The thing folks often miss is that wrapping and gloves only *support* your wrists - they don't fix underlying issues with how you're throwing punches or holding your hands, and bad form just gets reinforced every session until something really goes wrong. Before you decide between taking time off or pushing through, get someone who actually knows boxing mechanics to watch your technique, because wrist pain that's worsening suggests either you're loading them wrong on impact, your hand position is off, or your wraps aren't tight enough to actually stabilize anything (most people wrap way too loose).
If the form checks out and wraps are solid, then yeah, a break's probably necessary - but it might be just a week or two of modified training (heavy bag work without full power, focus mitts with lighter contact) rather than stopping completely. The real pitfall is waiting it out thinking rest alone will fix it when you go right back to the same movement that caused it.