Sorry you relapsed again. Glad you are back.
Succinctly, I don't think any type of mental health care is an either/or proposition. CBT is such a great tool - changing our thinking (I found the workbook exercises I did especially helpful as they are so specific) is something everyone can stand to assess, not just us alcoholics.
I've had non-med therapists (ie not psychiatrists), psychs who also talk and pastoral counseling over the years. Right now, the first and third w med checks for the second.
GOOD experts, especially with substance abuse training, have been the most important for me in sobriety.
To the "worse not better" thing...I have found that any help that's useful prompts discomfort since we don't like change - so whether that's "worse" is up to us, depending on if we are prompted to grow because of introspection, discussion, and revelation, or we reject it. Clearly, I find "better" the result of the good resources - I use that qualifier again because I've seen much less and much more skilled and productive folks over the years. Meds are another part of the discussion, and one I feel is important to examine.
Good luck - truly, good decision making and change wished for you, rather than luck.