There's a bit more to HIPAA than signing a BAA with your infrastructure vendor. I agree that you currently aren't storing PHI, so you're in the clear for now. I imagine that in the future your business would require you to. There's a bunch of things like auditing, logging, vulnerability scanning, disaster recovery, training and having policies in place when you do need to fully account for protecting PHI.
We open-sourced our HIPAA policies where I work at Catalyze recently. Check 'em out and good luck! http://catalyzeio.github.io/policies/