What is the best way to reapply for a denied Class 3 medical certificate?
Take steps and do your homework BEFORE applying for your medical through FAA MedXPress!
I suggest discussing your concerns with a qualified Aviation Medical Examiner or beforehand, assuming you are a member, with AOPA Legal and Medical Services. AOPA has an excellent list of resources on health conditions that may affect certification.
Because a possible history of counseling may qualify as treatment, consider the alcohol and drug abuse guidelines. Note the phrase complete abstinence.

1. To be considered for medical certification, you should write to the FAA, stating that you have completed at least one full year of recovery with evidence of complete abstinence after being treated for drug or alcohol abuse. Although the Part 67 regulations require that there be a sustained period of abstinence of no less than the preceding two years, pilots may be considered for recertification as early as one year after successful treatment with appropriate documentation.
2. The FAA will require the following:
a. Your complete treatment records and discharge summaries.
b. An evaluation conducted by a professional who has had training in diagnosis and/or treatment of addictions. These professionals include substance abuse counselors, psychologists or psychiatrists, other physicians with training in addictive disorders, or members of the American Society of Addiction Medicine (ASAM). (A psychiatric and psychological evaluation may be required if the initial evaluation is inconclusive).
c. Evidence of successful completion of an inpatient or intensive outpatient program with a documented commitment to abstinence.
d. Participation in an acceptable aftercare program consisting of individual and group counseling sessions for at least 12 months.
e. Establishment of a monitoring system that includes a physician with expertise in substance abuse disorders, and
f. Additional monitoring reports from employers, family physicians, or others, as well as alcohol testing when indicated.

The mental health section has a page on ADD/ADHD. Summary excerpt is below.

Because of the potential for significant underlying psychiatric or psychological problems and the side effects of medications, the FAA does not currently allow medical certification for a diagnosis of ADD/ADHD requiring the use of medication.
For medical certification consideration, you will need to have
discontinued all psychoactive medications for at least the preceding
90 days.  After being off the medications for 90 days, a
neuropsychological evaluation should be conducted.  The
neuropsychological evaluation must also include the following three
tests:

Trail Making Test
Wisconsin Card Sorting Test
Paced Auditory Serial Addition Test (PASAT)

If the airman is an adult who has been prescribed one of the
stimulant-type drugs for ADD, but has not been diagnosed with the
disorder, the medications will have to be discontinued for three days
before undergoing the neuropsychological evaluation noted above.

Because you may have a history of treatment with antidepressants due to the past prescription, the mental health section has a page on special issuance for depression with antidepressant usage. Summary excerpt is below with emphasis in the original.

Effective April 5, 2010, the FAA began considering individuals for
special issuance medical certification who are being treated for
depression with one of four specific antidepressant medications.  All
classes of medical certification will be considered, but individuals
who are granted a special-issuance medical certificate under this
policy may take only one type of antidepressant medication limited to
the following four medications: Fluoxetine (Prozac), Sertraline
(Zoloft), Citalopram (Celexa), or Escitalopram (Lexapro). All these
medications are SSRIs, antidepressants that help restore the balance
of serotonin, a naturally occurring chemical substance found in the
brain.
Increasingly accepted and prevalently used, these four antidepressants
may be used safely in appropriate cases with proper oversight and have
fewer side effects than previous generations of antidepressants.
While the focus of this policy statement is on individuals being
treated for depression, the FAA realizes that these four medications
may be used to treat conditions other than depression.  It should be
noted, therefore, that, in all instances, the FAA will continue to
consider applicants and make determinations on a case-by-case basis
under the special-issuance process just as it always has.
…
No regulatory changes are being made under this policy.  Further, the
FAA continues to believe that applicants requiring use of multiple
antidepressant medications or use of any other psychotropic medication
in conjunction with any one of the four specified in this policy will
not meet the criteria set forth under this policy.  The use of
psychotropic medication continues to be disqualifying under the
medical standards and special-issuance certification will be granted
only after thorough analysis of each individual case presented and
only when appropriate conditions and limitations are in place so that
the applicant may safely be permitted to operate an aircraft.  It
should be noted that as new information becomes available and
recommendations from the medical community change it may be necessary
for the FAA to again revise its policy.