My RDS is in a VPC, so it has a private IP address. I can connect my RDS database instance from my local computer with pgAdmin using SSH tunneling via EC2 Elastic IP. 
Now I want to connect to the database instance in my code in python. How can I do that?
Point your python code to the same address and port you're using for the tunnelling.
If you're not sure check the pgAdmin destination in the configuration and just copy it.
AWS - Connect to RDS via EC2 tunnel