Its a bit of as jumble...you say youre shy and awkward, yet you will happily chat away to the rest of the group - whereas Id have thought having a partner would have made it easier to mix and talk to other people.
noone is saying that when you go out, you have to be all over each other, but at least acknowledge him...what do other couples in your friends do?
Really think if you love him, youd spend quality time with each other, and knock the group thing on the head for a bit