Polyamory is like a big amplifier for your relationships. If your relationship is strong and happy, polyamory can bring out more of the strength and happiness. If your relationship is strained and unfulfilling, polyamory can drive the wedge in deeper.
I'm not sure what's suffocating you, but if you try to explore polyamory while you still feel that way, you may find the bag over your head gets a little bit tighter.
The earmark of a strong relationship is the ability to communicate with your partner. If you don't have good communication with your partner, then 10 years is enough time to have built a solid enough foundation from which you can start learning to communicate. I suggest talking to your partner about how you feel. Perhaps a counsellor can help you learn to communicate together.
Get to the bottom of what's missing in your relationship. I have never seen a relationship where the thing missing was another person, so don't think that exploring polyamory will solve anything. If there's something missing in your relationship, then it must be found within your relationship, not with someone else.
I don't need labels to define me. They're sticky and I hate the glue they leave behind.