Is it normal to randomly get distant/easily annoyed with those you’re closest to?

This is a topic I'm not sure I'll ever get tired of addressing. I spent many years myself feeling as if there must be something wrong with me when I just wanted everyone else to go away. Just as you have described, it wasn't necessarily that anyone had done anything to annoy me, but sometimes it just felt like too much to be around people. It was like I couldn't hear myself think, or at least I couldn't get a handle on organizing my thoughts. 

But the answer is, yes, this is perfectly normal. It happens to everyone, it just so happens to occur more often for some than it does for others. 

While there are many different explanations for why this occurs, one of the more common comes out of the work of Carl Jung and has been popularized by the Myers-Briggs Type Indicator personality assessment. That is the concept of Extroverts and Introverts. 

It's very likely that you heard people talk about this concept. What many people don't realize is that there is, what I'll call, a "pop-culture" understanding of these terms and then there is a less understood but more clinical definition, and they are significantly different from one another. The pop culture view is that extroverts are outgoing, charismatic, life-of-the-party types. Introverts are shy and awkward and quiet. Everyone wants to be or spend time with extroverts, "they're the best". Nobody wants to be labeled an introvert because they're just awkward. But from a psychologically clinical standpoint these terms aren't about how we behave in social situations, but in how we prefer to interact with the world around us. Extroverts like to focus on the outside world. Extroverts enjoy “being out”, engaging in activities that involve large groups of people, and maintaining as many social connections as possible. They draw energy and inspiration from being around other people.

Introverts, on the other hand, enjoy focusing on ideas. They like to spend time with their own thoughts and while they still need social connections they prefer to have fewer, but deeper, social connections. They draw energy from quiet spaces and having deep, meaningful conversations with the few people they most trust. A person can be very socially awkward and shy and still be an extrovert because they love being around other people and get energized from being at a party. And just the same, an introvert can be very charismatic and appear to be the life of the party, but they will be emotionally and physically exhausted from all those interactions.

At the end of a long stressful week of work an extrovert is looking forward to getting together with a big group of friends to go out to dinner, and then a concert, and hopefully an after-party. That's what they need to relax, re-energize, and get mentally ready for another work week. At the end of a long stressful week of work an introvert is looking forward to grabbing some take-out, going home, and settling in with a good book or TV show, taking a bath, or something of that nature. That quiet time to be alone is what they need to relax, re-energize, and get mentally ready for another work week.

It's important to note that people are not strictly one or the other. It's a scale. A few people lean strongly to one side or the other, but most land somewhere in the middle. Sometimes they want people around, sometimes they don’t. Even if you generally identify as an extrovert, you still need short stints of quiet, every human being does. 

So don't ignore that need. Give yourself permission to take some time alone to do something you enjoy. You'll find that it will help alleviate stress, make your social interactions more enjoyable, and help your energy levels overall. 

I hope this helps you find an answer to your concern.