First, I don't think the stressful situations (moving etc) can be blamed for much, if any, of your conflict. And I don't things things will settle down when your lives are more regular. You're still in the first few years of your relationship, and if things aren't happy now, they're not going to suddenly become happy because of some external factor.
experiencing your marriage right now
. This is what your marriage is.
The first eight years of my relationship with my spouse were long distance, so this is coming from someone who has kept a relationship successful despite that factor. Mind you, my needs seem to be very different from yours: I don't need a lot of attention or affection to feel loved and valued.
I think it's great that you can identify some of the needs you have, such as insecurity, and that you can identify some of the negatives (in his perception) which you might be displaying ("clingy and needy"). That's actually a great jumping off point for a real and helpful discussion about your relationship.
My approach would be to go out for coffee when you see each other next, and to start out the conversation by saying "I realize I've been acting clingy and needy when you're around. And that must be really stressful for you when your only time to relax is when you come home. I was hoping we could work together so I can make you feel more comfortable, so we can be happy when we spend time together."
Assuming your husband cares about you, which I'm sure he does, this achieves a few things:
1) It makes it clear you're thinking about his needs. Yes, you have needs as well, but that's all he's been hearing about lately and even if he's taken time for his own needs, it probably feels to him like he hasn't been able to address them properly. So taking some time out for his needs, and temporarily setting your own aside, is a healthy thing to do, and gives him the opportunity to go on to point 2 (below).
2) It makes him want to return the favour. This isn't the primary goal here, since you really should be genuine about wanting to make things better for him, and putting his needs on at least as high a level as your own. But if your needs were addressed wholeheartedly right now, wouldn't you feel like you wanted to return the favour?
Healthy relationships stay healthy because both people know, from their history together, that the other person cares and wants the best for them. You guys haven't had time to really build that yet, but you will. And it looks like this time it starts with you: Go ahead and want
the best for him. Make it clear you're trying to address what he wants and needs out of your relationship, so he feels secure and confident enough to do the same for you.
There is, of course, a chance that doing this won't work (it definitely won't work if you aren't genuine, but even if you are there's a chance of failure). If that's the case, you may need to have a discussion about your needs so the relationship doesn't become one-sided. If that happens, I think the important thing is to talk about it before
you've become upset all over again by the situation. In other words, be direct about your needs, but not emotional right off the bat. I might say "I'd really like it if we could cuddle more before we go to sleep at night. I like it when we do that." Or perhaps, "It makes me feel really loved when you think of me and pick up an extra coffee on the way home."
Something I do, probably out of habit at this point, is thank my husband frequently when he makes me happy. Not every single time or anything like that, but I'm often saying things like "thanks, I really needed that hug," or "aw, I love it when you tell me you love me; it makes me feel all warm inside." I rarely have to ask for attention, but I get a lot of it. I guess I make it worth it and enjoyable for him to give me plenty. But more importantly, I get the full enjoyment out of each experience, because I get to return that joy to him, too.
Anyway. I hope I don't sound all holier-than-thou or anything... I'm naturally less in need of attention than most people, but that has its downsides too. I think the long-distance element can work very well and my experience has proven that, and I bet you can make it work for you too. The important thing is knowing what your needs are (which you do) and being able to communicate them to your spouse.
I hope everything works out for you and that you and your spouse both see your needs met and a happier, less stressful relationship soon.