Hey alilgoat well I did some online research and found out for you, that dreams about choking (the softball stuck in your throat) means you are suppressing your emotions (possibly about being so far away from your wife and unborn child). Think of that phrase, "all choked up." You may be intentionally holding in your fear, anxiety, frustration, sadness about being so far away from your wife. And since you are with other soldiers, maybe you feel like you can't express these feelings for fear of being judged or ridiculed or something? Just guessing...
It totally makes sense that you're having these choking dreams. Don't repress your emotions. That's not good for your mental well-being.
So, that's why I think that the softball is a metaphor or symbol for your emotions that you are choking back. That's my take on your dream. It's your subconscious mind telling you, "Hey, buddy, stop repressing these emotions." It's probably why you wake up gasping for air.
I hope you can find a way to get those emotions out. Even if its just sending a message to your wife and tell her EVERYTHING that you've been repressing (hence, these choking dreams).
Maybe that will make you stop having these choking dreams, and make you feel better overall.
And, thank you for your service. *salutes you*