Can we get a patent for a cloud service?

I concur with Allan. The Alice v CLS Bank decision changed patent law quite a bit regarding software patents but it is not correct that software-based technologies cannot be patented; we just need to be much more particular about them now. The key point to keep in mind is that in order to be patentable your invention needs to have some aspect that is both new and not obvious from what was known before. If your invention uses cloud computing to conduct the same personal health monitoring process as was done in the past then without more detail it sounds to be obvious and not patentable. If there's something else that's different that something else may give you a reasonable basis for actually getting a patent granted.
Alternatives to patenting generally offer less protection: software is subject to copyright protection but that's narrow and often can be easily designed around. It protects you if someone actually copies your code, but there are open source license issues that come into play if you used some open source code when writing your program.