Well, it all depends on how loud you want your music. If it is not loud enough for you, pick up an amp. It probably doesn't get enough power, but I'm not sure why your computers can't power 16 ohms, that seems a bit strange to me. But yeah, get a cheap amp and you should be good to go.
Impedance alone is not always the determining factor for how hard headphones are to drive, while it can be a good rule of thumb for determining how much power you need, headphones that are low impedance yet relatively hard to drive do exist. Most COP owners generally recommend using at least a cheap amp such as a fiio E6 or using a music player with a relatively high output integrated amp like a Cowon or a Sansa-clip.
If you're looking for something relatively cheap, a Fiio E10 should be more then adequate. If you want something really nice that would be suitable for higher end end headphones should you decide to get into them, I strongly recommend considering the Schiit Magni amp and Modi dac.