Ok this has really been bugging me. In Skyrim you are dragonborn but playing Oblivion I got the vibe that the Septim's were the only dragonborn. But that outs a damper on my Skyrim because I am an Argonian and do not know how he could be related to the Septims. How is your character dragonborn i'm pretty sure there is a logical explanation but i do not know it.

Check these out

http://www.gamesas.com/topic/1235448-breton-as-dragonborn/
http://www.gamesas.com/topic/1388717-what-is-the-dovahkiin/
http://www.gamesas.com/topic/1237986-what-is-dragon-blood-and-why-is-it-required-to-wear-the-amulet-of-kings/
http://www.gamesas.com/topic/1252756-is-the-dragon-born-the-reincarnation-of-tiber-septim/

Dragonborn-ness is not hereditary. The Septims would take up the mantle on coronation.

You're question should lie in "How can the dragonborn be a Shezzarine and dragonborn at once?",

Or, where does the Dragon Blood come from?

No, dragonborn does not essentially mean a septim, besides even if it is, the child follow the mother race. so say, if a septim slept with an argonian then the child will be an argonian.