When you Google for Myers-Briggs, you will find several incarnations of the test on the web. I also remember a Facebook version making its rounds a year or two ago. I'm not sure how independent their engines are, though.
As to your changing test, I wouldn't make too much of it, for two reasons: First, although Meyers-Briggs is better than astrological charts (which are garbage), it's still not an exact science. Second, real-world personalities fall onto a continuum in each of the test's four dimensions. Your character may be somewhere in the middle of each continuum. Nevertheless, the score only provides for one bit in each dimension. Both issues conspire to make your score less of a clear, objective test result and more like a four-times coin flip. Your changing result, then, may just reflect different flips of the coin, rather than a true change of your personality.
So as you search the web for Myers-Briggs, maybe you can look out for a variant that tells you the strength of the outcome in each dimension.