Hi, I'd like to help you with your question.
Avoidant personality disorder is based on deep feelings of inadequacy and fear of what others think of you and what you do. This can cause you to want to avoid others, which in the Navy is very hard to do.
If you are not already in therapy, it may be a good time to try to get help. I understand that getting help for your problem may be hard to do, but Avoidant Personality disorder is best treated with direct therapy. The good news is that you are aware of it and you are open to seeking help (from your willingness to reach out today). I know seeking help in the Navy is easier said than done (I have a close family member who just completed his 20 as an enlisted so I understand), but if you can, make the attempt. If you are unable to or feel too uncomfortable trying, medication and self help can make a big difference until you feel better seeking therapy.
Anti anxiety medications can help you cope with the fear of others. It is not recommended you continue on these medications if you have access to therapy, but in your case you may have trouble having access to therapy and privacy is difficult so medications may be a good short term solution. Also, try self help. Here are some resources you can use until you can see someone to help you:
The Cognitive Behavioral Therapy Workbook for Personality Disorders: A Step-by-Step Program by Jeffrey C. Wood
The Hidden Face of Shyness by Franklin Schneier and Lawrence Welkowitz
The Emotionally Unavailable Man: A Blueprint for Healing by Patti Henry
You can find these books on Amazon.com or any local library may have them for you.
I hope this has helped you,