Yes I used to be shy at work - am naturally introverted and what I thought was just keeping myself to myself and getting on with work was coming across to others as me being stuck up and unfriendly... 
I'm better now, would still probably naturally prefer more of a quiet working environment than the 'we're mad here' loud bubbly in-each- other's-business kind of team you describe (you have my sympathies!), but I have taught myself to get on well with all sorts of different people. What helped me was getting really really good at small talk, so as to avoid any awkward silences (well, what others perceive as awkward, see above
) - I've got a whole range of uncontroversial topics now ready to start a light conversation on, TV, holidays, weather that kind of thing. It doesn't have to be super personal 'OMG' drama stuff....
Also I take advantage of the fact my analytical brain is good at retaining facts and remember lots of details about my coworkers partners, families, hobbies and so on, so I'm able to ask them lots of questions about themselves, their weekends etc which most extroverts like answering - in fact most people like talking about themselves and appreciate you showing an interest, so so long as you read any hints that they aren't comfortable answering certain things, you're usually onto a good thing there! Or if need be I share fairly mundane info in exchange about my own life - like you I don't like oversharing but it's nice to talk about things like what you plan to do on your holidays etc.
I suspect I would still be seen as one of the quieter ones on the team, possibly a bit 'boring' and to some extent it feels a bit false as I do tend to fake a bit of interest in some things which I actually find a bit tedious (like other people's holiday plans
), but at least I don't get called 'up myself' or snobby any more - to my face anyway
. You sound like you are getting on fine, not everyone can be the loudest one (and for some reason people do like to point out to shy people that they're being really quiet, I don't know if they think it'll somehow help or what
) but it doesn't mean your teammates are actually annoyed by it?