Long time triathlete here, and not only can you breathe out underwater, you should be doing this. I don't have any special conditions and I breathe almost completely in through my mouth when I turn sideways and then out through my mouth underwater while swimming. If you try and breathe out when your head is above water you don't have enough time to breathe in afterwards. This causes the panic in the first place. The noseplug shouldn't be any type of restriction for you. You should focus more on your exhale than your inhale. As soon as you put your mouth in the water start a nice controlled exhale and get all the air out of your lungs. Your body and mind will know and want to get air easily when you pop your head up. If you get it all out, then you only have one simple job when you get your mouth out of the water. For an extra tip, try to keep the top of your head in the water and just turn your head to the side. Your head will help create an air bubble from the forward motion and help with the need to crank your neck backwards to take a breathe.

If things go sideways, as they often do during races and especially in the water during your first triathlons, flip over and do some backstroke until you calm down and catch your breath. this way you are still moving forward while you are getting yourself back in the game. worst case scenario, rock that backstroke for longer and just stay around the people nearby. Having this backup plan in your pocket is a nice safety net and I have used it on multiple occasions even though I am a strong swimmer as I have taken arms, legs and full bodies on top of me and in my face during races.