I think it's a high risk/low return idea to make ourselves compatible with the welif's body.
Evolving takes time. I don't think we have time to evolve while drowning and currently immersed.
Even if we could instantly 'become one' with our critter's circulatory system, or better yet gain the ability to absorb oxygen from another creature's circulatory system, that has very limited benefit to us right now. If it could constantly breathe, then it could replenish the oxygen we take. Right now it appears to be submerged, as we are.
We were trying to severely injure our log, fatally if possible. We cannot tell if we've hurt it enough for death or incapacitation yet, but we do appear to have driven it into a frenzy. Creatures that 'freak out' underwater rarely behave as expected (creatures that panic rarely behave as expected anywhere). We cannot count on our log continuing to breathe properly, so any oxygen in its blood must be considered a very temporary non-renewable source. Plus it's moving strenuously and it's bleeding - two things also likely to rapidly decrease the available oxygen in its body/bloodstream.
We don't need nostrils on our tail, we have insect-like breathing openings at 'unspecified' places on our body - we've also been told before we burrowed most of our body into the log that most of our body had been sticking out of the creature - and that our body was completely submerged.
The creature is thumping against something hard and 'frantically trying to dislodge' us. That may or may not be the behavior we are hoping for - of a creature so agonized and/or injured that it can make no effort to catch or harm us as we escape.
We also do not know several other very important details: How deep is the water? Are there any caves that the creature might have carried us into, and if so, could they be complex or contain things that could slow our escape? Are there parasites or predators in this water which might be powerfully attracted to the blood?
I'm going to guess that we have stayed as long as we safely can - that we are somewhere close to the balance point between 'staying longer means we are increasingly unlikely to get to air in time' and 'if we move away from the welif it will almost certainly catch us'.
I'm going to hope that a) the wound hurts like crazy and b) there's enough blood mixing into the water from the welif that IT can hardly see/smell/taste/otherwise sense much other than its blood and won't be able to latch onto us even IF it still has any intention of trying, and c) that we have some way of telling the direction the surface may be in. We... don't actually know if we are buoyant or are more dense than water... though MOST worm-shaped creatures can undulate, a motion that's good for moving through liquids even if our many many legs cannot find any leverage to push against.
Rapidly exit the creature's enlarged opening and continue to rapidly move away from the creature. Once more than 3 of our body-lengths from the creature, attempt to find the surface/shore.