Although a private counselor can make your journey smoother by providing a “road map" to help you to navigate the admissions maze, you are absolutely NOT at a disadvantage if you tackle the process without paid assistance. Instead, you can seek out free information online at College Confidential and elsewhere. You should also pay close attention to the advice and instructions for international students that you'll find on college Web sites. But, as you do so, keep in mind that this can be a very inconsistent process, so never assume that every college's policies, requirements, deadlines, etc. are the same.
When it comes to recommendations, colleges actually don't want a reference from a paid independent consultant, and so submitting one might even work against you. References should come from teachers and administrators at your school. Since you don't have a guidance counselor as most U.S. applicants do, you can seek out another school official who knows you well to complete your school forms and to write on your behalf.
Although some private counselors boast that they have connections in admission offices and can help facilitate your acceptance, this is NOT true at the most sought-after, selective schools. In fact, revealing a connection to a private counselor can occasionally work against you, too, because some admission officials favor applicants who have not received paid assistance. So, despite the fact that private counselors can make a complex process easier to understand, you gain no advantage at admission-decision time through hiring outside help.
The biggest problem I've observed when working with international students is that many of them overestimate their admission chances at highly selective schools. The colleges and universities that are best known to most international students are those that typically deny 9 or 10 qualified applicants for each one who is accepted. Moreover, the bar is set even higher for international students who require financial aid. Yes, there is a very short list of U.S. college that are “need blind" and thus do not consider a student's ability to pay when making admission decisions. BUT these schools are among the most competitive in the world, and many international students apply to them because of both their prestige and their need-blind policy, making these schools even more competitive. So I always encourage international students who require financial aid to be certain that their college lists include institutions where the typical admitted student has grades and test scores that are well below their own. Also, keep in mind that the majority of U.S. colleges do not offer any financial aid for international students. So, if you will be applying for aid, it's critical that you aim for those places that have funding available and that you understand how hard it is to get it.
Good luck to you as you continue with your college process. You can certainly handle this on your own and there are even advantages to doing so, but just be wary of the pitfalls you may encounter.