I just have the one DS - I've never had a problem with the term "only child" to be honest, though I guess I tend to say "we've just got the one". I suspect he'd find "solo flyer" a bit patronising, but then he's 14 which makes a big diference.
I do think it makes for a different relationship - I was one of 3 and a lot of the time "the children" were doing one thing, or had one set of rules, and "the adults" did things differently. That's never been the case with DS, though we are still the adults and get the final say on rules etc. But we tend to all do things together, or else do things independently, and we don't have that same distinction into separate groups, which makes us more like 3 individuals with relationships between us IYSWIM.
It has also meant that we can make choices on the basis of what suits DS (and me and DH) without having to worry about being "fair" - if there is money and time to do something, then we can make that choice without worrying about how anyone else will react.
We're certainly all very happy with this set-up, and I don't think DS has missed out on anything particularly by not having siblings - he has always been very involved with groups where he had to get on with different personalities, share, take turns etc, so he didn't miss out socially.
It may feel very different when it's not your own positive choice though - you maybe need to go through a grieving process for the children you thought you would have but now can't. Obviously that's not like losing a child or a pregnancy, as they were only "theoretical" children, but coming to terms with not having something which was part of how you saw your life progressing is a similar process. Once you've dealt with those feelings, I'm sure you'll be able to feel positive about the new pattern your life is taking.