Dropbox is one of the most popular cloud storage services available. It offers a HIPAA-compliant secure storage option meaning Dropbox, in conjunction with PicSafe, can use used to help you comply with HIPAA and HITECH. Please see the HIPAA/HITECH section of the Standards and regulations page on their site. See their "Getting Started with HIPAA" guide and Help Center article for more detailed information.
The "Dropbox Basic" free plan, may be all you need. That gives you 2GB of storage which should be enough for roughly 4,000 photos. If you require more storage space, you can upgrade to various paid plans.