Kristina,
The worst thing that can happen at an Apple store is that they offer you an estimate for repair/replacement and then refuse it after they look inside your phone and find non genuine Apple parts.
Your are very fortunate to have warranty and apple care on your phone and therefore as Kenny stated in an earlier post, you shouldn't even try putting it in a freezer for fear of invalidating that protection.
However, there are many people on this forum who are not in that fortunate position and error 3 seems to be so generic that even Apple techs themselves cannot give an answer except to suggest a 'hardware fault'.
I took my daughters Iphone 4S to the store and told them upfront that it was a 'refurb' phone purchased before Christmas, without any Apple warranty and all I was seeking was to have the software restored to an earlier version, not a handset replacement. They told me they could not do this, which wasn't that surprising as Apple have put much effort into recent IOS versions to ensure phones cannot be restored to earlier IOS releases.
I had to take them at their word that the phone was faulty because I could not prove otherwise and they would not assist with this. Apple seem to have it well stitched up..
Anyway, a 12 year girl does not understand the frustration of all this poor support service which doesn't do much for the 'older phone' sector. Her phone worked before the update and then would not work after the update, so she is now the proud owner of a new Iphone (complete with Apple warranty) and I am the poorer for my false economy.
Unlike your well justified opinion of these phones, I could not convince her that Iphones were 'crap'