Starting with the caveat that I'm not a doctor but someone that does a lot of cold-water diving...
Thirty minutes of uncontrolled shivering is an almost certain indicator of hypothermia - a potentially fatal problem and true medical emergency that requires immediate attention. If your choice is between freezing and fizzing, you need medical help. Pronto.
Cold-water diving requires divers to exercise greater care than warm-water diving. Safety requires that cold-water divers stay warm, reduce pO2 limits, and decompress more slowly. At its most extreme, cold-water diving should be considered technical diving due to the additional equipment, training, procedures, and risk it involves.
Cold causes capillaries in the extremities to contract, a two-fold problem for divers: the reduction in blood flow limits the ability of the surrounding tissues to off-gas, thus extending decompression times, and; the smaller capillary diameter makes it more likely that small bubbles will be entrapped in the peripheral tissues, further blocking blood flow and potentially leading to full-blown DCS. Nonetheless, shivering is not recommended as a treatment for hypothermia - getting warm is.
The conflict (and your question) originates in the effect of sudden reheating (through exercise, hot showers, whatever) on the blood supply and off-gassing potential of the peripheral tissues. Remember the Coke analogy: the CO2 suspended in the soda will off-gas slowly at room temperature but will fizz aggressively if the bottle is agitated or warmed quickly. Frighteningly, shivering may effectively combine both.
Stay warm.
Steven