Escaping a sunken ship or submarine has some similarities to an emergency ascent in the course of SCUBA diving, but it's not identical to it.
First the differences:
You don't have fins. Without fins, you cannot swim as fast and as efficiently. Fins allow you to limit oxygen consumption by using efficiency-optimized leg muscles. Swimming with arms and feet takes far more energy for less speed. A 100 ft swim is still manageable, but now it depends a lot on your physical (and mental) condition.
You've only been under pressure for a short time. Otherwise, it's almost certain that you would have already drowned. Surface ships can trap pockets of air, but generally they fill up with water quite thoroughly when they sink. Nitrogen loading is determined by time*pressure, not just pressure, and won't generally be a concern.
Submarines are equipped with emergency escape gear. The gear comprises a basic airtight suit with a compressed gas bottle (and a pressure relief valve) to fill it up and produce an extremely rapid buoyant ascent. This allows for ascents from 500+ feet.
Note that submarines also sink differently from surface ships. A ship will equalize to ambient pressure once underwater, as nothing inside it can resist the pressure difference. A submarine will maintain some compartments at near-atmospheric pressure. This delays any nitrogen loading before you actually exit the sub.
Since submarine escape gear supplies one with compressed air, allowing plenty of time for the ascent, DCS is again a concern. In that case, DCS is avoided by ascending as fast as possible - about 80 m/min, 4-8 times faster than when diving - to minimize the amount of time spent of high pressure. The same feat, going fast (in both directions), is what allows freedivers to dive as deep as 100-200 m and come back up without need for spending time in deco.
One thing that's more similar to escaping a sunken submarine than any kind of diving is escaping a sunken submarine. All boat crews and even contractors that go out to sea trials generally receive submarine escape training specific to the boat they're on and the gear it's got, so you'd follow that training.
The similarities include:
Lung overexpansion injuries are possible with even small amounts of compressed air. You need to keep your airway open (exhale). As the water is filling up your vessel, it's equalizing its internal pressure up to the higher ambient pressure. So, if you've taken any breaths on the bottom, you've breathed in compressed air.
Passing out is caused by hypoxia, not by ascent speed. Hyperventilation is useless in a survival situation, as it simply tricks your body into delaying the urge to breathe. That's not needed, as exhaling during the ascent will already do the job of controlling your breathing. Additionally, a dangerously high blood level of CO2 (hypercapnia) takes much longer to reach than a dangerously low blood level of oxygen (hypoxia).
In a scenario less likely IRL (but more likely in a movie), with a large vessel where you have managed to survive on large pockets of air, that air has been compressed to ambient pressure. That turns it into a SCUBA-like scenario where eventual DCS is possible. However, you cannot deco without breathing gas, so there's no choice about it.
In conclusion, your top priority is to reach the surface on your remaining blood oxygen. Hypoxia leads to loss of consciousness, which leads to drowning.
Your second priority, if you're starting the escape on a full breath, is avoiding lung overexpansion injuries by keeping your airway open. Lung overexpansion injuries have a lower fatality rate than drowning.
Avoiding DCS is not a priority at all, because you don't have a compressed air source to buy a meaningful amount of time for deco. Slowing down your ascent so little that you can still do it on one breath will do nothing for you, except increase the risk of failure and drowning. Fortunately, over 90% of DCS cases are survivable.
All in all, you want to get the best ratio of ascent rate to oxygen use rate.
If possible, grab any available buoyant object, because that allows you to ascent with minimal effort.
Absent that, get out and swim up. If you don't get up to speed with buoyancy and light kicks, active swimming will have you use up your blood oxygen at maximum possible rate. In that event, you might as well use your muscles' anaerobic energy stores. Practically, at that stage, you won't be thinking about it anyway.