Yes it is your fault. You are responsible for yourself and to not panic- even when things go bad and gear does not work perfectly. If you get hurt or killed in a dive accident, it is not going to matter too much whose fault it is, gear or diver... the correct way to look at the situation is to figure out how to deal with it better the next time. Asking: "was it my fault or the gear's fault?" is NOT the right question.
For example, the fin strap on a rental fin snaps underwater... Is that the rental company's fault, or the diver who failed to check it adequately... It doesn't really matter at the time of the incident, the important thing is to deal with it without getting hurt.
However, the OP should be happy that they got to experience a somewhat out of control situation early in their career. The fact that they panicked and required assistance is not good, but they were apparently able to calm down and enjoy a second dive on the same day is significant, many people could not do that. Being able to regroup and do another dive is a huge accomplishment!
This is the EXACT way people learn to dive and to deal with problems! The feeling of panic and out of control situation, should be remembered for a long time and the diver needs to formulate in their mind exactly how they will deal with this situation and how to NOT panic, if/when it happens again.
Dumping too much air on ascent, happens to everyone. It is a skill that takes time and patience to master. If you were half way up, dumped a lot of air and were" falling hard", then chances are the diver is somewhat over weighted. Perhaps look to carry a little less lead?
As for the suddenly wet breathing regulator? People have already made a lot of good suggestions, but regardless of what the cause is, the diver needs to know and be able to implement an effective response that circumvents the panic cycle of increased stress. Regulators can have problems, but the diver needs to be capable of effectively dealing with it- we can worry about "whose fault it was" on the boat, after everyone is warm and dry.
FYI, the first thing you can do if a reg is breathing wet is to press the purge button and try to get a couple of clean breaths. Even if it is actually leaking badly, you can breath from the freeflow without taking on water. Practice that a bunch if you are not confident in your ability to do so.
Second, the appropriate response to a problem second stage, leaking water for example, would be to switch to the octopus if the problem does not resolve itself. That should be done before looking for help from others. A diver needs to be able to handle these switches, even when stressed - their life could depend on it. Of course, it would be fine to simultaneously signal to the buddy that you are having "issues", but being able to master your own gear is of primary importance.
Another thing the OP, should learn from this situation is exactly how things spiral out of control. Dumping too much air (probably being too heavy), over exerting while kicking, not immediately putting some air back in BC, all of a sudden getting a wet breathing regulator (whether that was diver error or not), this stuff is all cumulative and it is VERY EASY to become uncomfortable and then quickly overwhelmed - sinking and not being able to breathe is NOT a good feeling for anyone. It is unnatural and SHOULD scare you a little - so getting freaked out is not unexpected for a very new diver.
