A couple of answers and comments have mentioned the fact that many current bioinformaticists are self-taught and do just fine. But bioinformatics graduate programs didn't exist ten or fifteen years ago when current, experienced informaticists were learning their skills. I would ask if that's still likely to be the case five or ten years from now -- or even if it's the case right now. I perceive that full-featured informatics software packages are becoming more user-friendly, and that it's getting harder for pure biologists to get useful things done with basic scripting skills without someone saying "why don't you just use <package>?"
So, since informatics really has become its own discipline, the question to address is whether you would enjoy inhabiting that field, going to those conferences, and collaborating with those colleagues more than you would enjoy remaining in biology and hanging out with the most computationally-oriented of the biologists. As a biologist, you can certainly enjoy informatics and incorporate it heavily into your research. But if you're truly becoming more interested in the development of algorithms and software than in the application of them, then you're already halfway over to the dark side...I mean, the CS side. ;-)
I can't speak intelligently to the problems of switching programs at a given school or with a given visa status, so I won't come down on one side versus the other. If someone offers you an easy transition to a more CS-based program, it sounds like it could be a good fit, and they would probably eagerly welcome someone with a strong biology background. But if it's a major issue to switch, then I'd at least give it another year to see how well you can steer your projects toward your interests without leaving your current program.
Just take a look at all the methods papers and software packages out there that are written and maintained by "biologists", some of whom put out a little code on the side and some of whom have turned to developing software full-time. If you code something useful and publish it, people might pick it up and use it, or they might not. However, if you then immediately have it used in five high-impact papers because you're collaborating closely with a number of biology projects, you will already be building your reputation as an informaticist no matter what your diploma eventually says!