Psychiatrists have their place. The chances are virtually 100% that your therapist is associated with one (to prescribe meds) so you don't need to seek one out.
I have had problems with anxiety and depression for decades. I take an antidepressant every day and it changed my life for the better. I feel perfectly normal, but I don't experience the multi-month periods of "down" like I used to. YMMV.
My mother took her own life at 50 as a result of depression/anxiety, and it's important to understand that 1) it's a real thing and 2) like many medical conditions it can be treated. A competent psychiatrist doesn't just hand you a 'script for something. Mine interviewed me for a full hour, going over what my therapist had told him, before settling on which medication to try.
Paula, especially considering your experience with alcohol, I think seeing a shrink is a good idea. Alcohol is a depressant, and it affects your thinking and biology long after you quit.