Besides being a character trait, is there any mental disorder that could be related to being an extreeeemely sore loser yet not having a big ego?

Sounds like: There are some things to explore with a therapist.A good rule of thumb is...When your feelings are too intense that they feel overwhelming ...Where they control you...Seek help.

Not really: You've got it that it is you and that you have control over it. You can go to couseling to overcome these insecurities and trait problems.

Passive aggressive: behavior may be what you're describing. Society teaches many of us to repress anger so we're reluctant to speak up when we feel offended. Like a chemical reaction, this always produces resentment, holding it in but expressing anger indirectly, often unaware of it. A sore loser views losing as a big deal but is it? Learning to speak up & to work thru defeat are good therapy topics. :)