If you're interested in joining an NPC sorority, go for it! Your membership in your service sorority can only help you. Lots of people do both.
Don't worry about mixers - you won't be required to go to any given mixer. You may be asked to participate in a certain percentage of social events, but those include formals and date parties; this is how my chapter did things. An option to consider with the mixers is just going for the first hour or so, before anyone gets too drunk.
As for your service sorority, I'm sorry that things aren't working out better
and I hope you can turn things around.
Take care.
