Hi there,
You have to be careful here, as you don't want to cause long-term damage. When you're carrying your guitar, make sure your shoulders are relaxed.
If you haven't already, check out the different ways to hold a guitar here. This video is one of Christopher giving advice on how to hold the instrument: https://www.guitartricks.com/lesson.php?input=13958&s_id=1141
Another piece of advice is that it's okay to move your thumb from the middle of the back of the neck to grab notes that are a bit more difficult to reach. Your thumb's position while grabbing a chord or playing a lick may contribute to the awkward feeling. Play around with your grips, and see what works! The important thing is to not feel tense.