I don't think stress leave would apply, because the stress is due to things outside the workplace, not caused by something that happened at work IYKWIM.
Stress leave is usually for work-related stress. If the job is making you sick, the organisation needs to do something about it.

Can you talk to a manager and be re-assigned? Stress isn't good for you or your baby. Can you talk to a doctor - a doctor's certificate/letter may help back you up? If you're part of the big 4 - they usually spout family friendly work policies. Is HR any use in your company? The last thing a company like that wants is the PR fall out of a pregnant woman breaking down at work. Even if the doctor says you can only work X hours, it may help reduce the stresss. Many companies will take as much from their staff as they can - including 15 hour days - it's up to you to stop it now.

Politically - it's better for you to be reassigned now (based on your pregnancy/stress), than have you boss think you're failing at yor job - it may affect your return to work chances.

Remember rule #1 - always look after yourself first.

Good luck