Of course you can be a loner.
In fact, if your loneliness stems from relationships that just "don't work out" with people outside the Church, it might be for the best.
Sometimes, keeping distant is a good thing.
Afterall, you are not meant to fit in with "society" in general. You are not "of this world".
However, this doesn't mean you hate or judge others....it simply means you don't fit in because perhaps your morals are different, or your interests are different, or.....
As for the Church family....yes, we see each other on Sundays. Some take on extra roles, cleaning, purchasing supplies, working in the kitchen, teaching, serving in the Altar, etc. However, not everyone picks up an "extra" role. Many merely come to pray, partake of Sacraments and then leave until the following Sunday. There's nothing wrong with that, either.
The Church is comprised of many personalities, and perhaps the fact that you are a loner (maybe even prefer to be alone) means you are destined to do something different for the Church. Perhaps write - theological materials one day, or even greeting cards for the shut-ins and sickly.
There are so many different ways we can serve the Lord. Don't count yourself out, just because you are uncomfortable around others.