"I'd like counseling" is more than enough reason to book an appointment, and perfectly acceptable reason to make that phone call!
If you think you want medication, you want a psychiatrist. Anger, short temper, easily frustrated when you used to be easy going CAN be signs of depression or anxiety (I'm not a doctor, and not diagnosing you) so even if you think you aren't depressed, or that medication won't help you; it doesn't hurt to visit a professional who can help determine what is best for you to do next. I see my psychiatrist once a year, once we got my medication sorted out.
If you know you don't want medication, you are looking for a counselor/therapist. This could be a psychologist or a social worker, or some other things. My counselor is a social worker who specializes in trauma informed yoga therapy and EMDR for PTSD, she is not a psychologist. I didn't need a referral. I just called and said I wanted therapy. There are all kinds of therapists, most people start with CBT or "talk therapy"- but you can look for art-therapy, or like I did, yoga therapy (though we also do CBT and EMDR)
A therapist is good for someone who has deep rooted trauma, or for someone who is overwhelmed by the daily stress of life. If you are uncomfortable with your first appointment- just tell them that. "I don't really know what to expect here." or "I feel silly and don't really know what to say, but I've noticed my behavior change, and I'd like some help with this."
Therapy can be short term. When I first started, because it was for a major event I went 2-3 times a week. Now I go 2-3 times a year when I just need a few minutes to help recenter on the techniques I've learned to manage.
If you are employeed by a large company, see if you have an EAP "Employee Assistance Program". Your first few visits may be free.
Be warned, not every therapist is good for everyone. It sometimes takes a few tries to find the person you connect with for talk therapy.