Could my iPhone be a refurbished model?

Last year there were software problems with my iPhone so I sent it back to the shop I got it from and told them about it. The phone was taken from me and they told me to come back in a couple of weeks. So I waited and went back. They then handed me a box and told me that they had just replaced the unit. I noticed straight away that it wasn't apple retail packaging as it was just a black case sort of thing. I took the new phone home and it worked normally and everything and I though no more of it until earlier when I read something about apple replacing faulty iPhones with refurbished ones. Is this true and is there a possibility that I have spent the past year paying for a phone that wasn't actually new and was someone else's refurbished one.

Yes, it is a standard practice to replace problem phones with "referbs'. I referb means your phone was cleaned, tested as perfect, at a factory test bench… So not a big deal dude.

Of course it was a refurb. You sent them a used phone you got a used phone to replace it. That is the way these things work.