Thank you for your interesting question. Metallic taste in the tongue can be a very difficult problem to diagnose.
The common problems are due to dental issues or fillings, you could visit a dentist to have a look at your teeth for a start.
Then you could look through the list of your medications, vitamins, supplements and diet to see if any of them could be a cause for this.
Lastly, you could visit a GP to see if there is an infection that could be causing this.