Meetings are a huge time sink. Surely they can be necessary, but only if they have a purpose for everyone involved and are run efficiently. Oddly, poorly timed scheduling may be the biggest problem.
This SEI blog post has some actual data to back up what many of us already believed.
(Edit to more specifically address the question)
In the blog I make a few points about managing your time that I think are relevant.
I realized that I am unclear if you are still doing the technical work, or taking on more management work. They are two very different work styles. They are so different that I strongly urge people to avoid trying to do both.
1) You need focus time to actually get technical work done, everything else supports that effort. I've had the most success by declaring a "focus time", typically a block of about 2 hours, putting it on my calendar to block it, and turning off the phone and email. This is uninterruptible time. In a team environment, it is usually necessary to get a common agreement on that time.
2) If you are leading meetings, look into good meeting practice, including having an agenda, facilitating, finding a good time for everyone, keeping on time, and most importantly, only having people in that meeting that must be there. Meetings are about coming to a decision.
Moreover, a well crafted agenda can make it clear whether or not that is an appropriate meeting everyone's time. Personally, I found all these to be highly valuable for the introvert that is me. Well managed meetings made me prepared reduced stress.
3) many of the other communications and can be handled in a similar way, prepare for a discussion and keep it focused on the needs. In my projects, we set up specific roles to co-ordinate specific topics, such as design, technical support, product content. The roles made it much easier to know who to talk to, and most importantly, I (the team lead) didn't have to get in the middle of every discussion.
4) other "pop-up" communications can be managed with fixed "e-mail times" or phone call times. Structure your day to get these out of the way in a block. This tends to be most efficient. THis works best for reading e-mails, responding via phone has real time issues that affect the other party as well.
Introvert or not, structuring your day can make a huge difference in both your productivity and stress levels. But the final point is
5) All this requires co-operation and support from management. I stress the productivity because that is something management is unlikely to ignore. As Heinlein said" don't appeal to his better nature, appealing to his self interest gives you more leverage"