I would agree with the above post that for any decent graduate program, it's a near-certainty you'll need research experience to be competitive. Clinical experience can be nice to see, but is generally of far lower importance than research experience. This may mean taking a year or two to volunteer part-time or work full-time in a psychology lab, and/or pursuing a non-terminal and research-focused masters program. You certainly can try applying, but unfortunately and in all honesty, I don't know that it would be the best use of your money and time.
An ancillary bonus of attending a funded program is that by having funding for its students, it goes further to ensure that the program has adequate resources more broadly for its trainees. In unfunded programs, there may be more variability in that regard.
Edit: I would add that I might also consider broadening your application pool to include balanced Ph.D. programs.