You don’t describe what type of problems you want to speak to the psychologist about, but you mention a fear of dogs. There are different types of psychologists out there, meaning that there are different methods of dealing with “psychological” issues – talking it out, behavioral therapy, etc. Different problems can be best “treated” with different methods. Like if you are afraid of dogs, then behavioral therapy would help a lot with that since they try to desensitize you to your fear rather than simply “talking about it”. Does that make sense? Now if you have fears about a lot of things, then maybe talking about fear as a general would help, possibly in conjunction with behavioral therapy to deal with your most bothersome fears.
By the way, where did you learn that psychological treatment is free in EY?