I'm so sorry, that does sound pretty awkward. Maybe there are hangouts that she could be invited to, or ones where it's not too awkward for her to tag along, but you should definitely be allowed to go out with your group without her sometimes.

I'm the same way!! I'm not proud of it at all, but I'm definitely jealous when my partner goes out with friends to have fun and tells me all about it after because I feel left out and forgotten. Even if she sends me reassuring texts or tries to keep me in touch, I still feel cold and mean.

(!!This is the most important!!) However, I know these feelings are wrong and try my best not to let them affect her, and definitely not control her in any way. Your girlfriend should recognize and do that too. It's not fair to either of you, you both end up feeling terrible.