The Beach

BJJ is uncomfortable...really uncomfortable. People are always way more in your personal space than is socially acceptable, they're trying to shut off the oxygen to your brain, and twist your limbs. That can be stressful, but that stress will better prepare you should you need to defend yourself. How can you reduce the stress and become more comfortable being uncomfortable.
Control your breathing- If you breathe improperly to begin with you exacerbate the suffocating feeling
Keep one shoulder blade off the mat- Bringing one shoulder blade off the mat nullifies some of your opponent's ability to compress your diaphragm and torso
Do an inventory- If you can talk you can breathe and therefore what you're experiencing is more mental. Conditioning mental fortitude with a trusted training partner is the most efficient way to remedy this problem I've found. Something I've talked about with many training partners is "the beach". It's a place that you go mentally where nothing is as bad as it seems and you can have a conversation of "real" or "perceived" danger with yourself.