More formal word for "know-it-all"
Solution 1:
I think you are dealing with a real bad case of confirmation bias.
Confirmation bias, also called confirmatory bias or myside bias, is the tendency to search for, interpret, favor, and recall information in a way that confirms one's preexisting beliefs or hypotheses, while giving disproportionately less consideration to alternative possibilities.
That being said this person is clearly unqualified to make OR deny a diagnosis.
References:
https://en.wikipedia.org/wiki/Confirmation_bias
https://en.wikipedia.org/wiki/List_of_cognitive_biases
Solution 2:
If you want to appear to be compassionate and understanding (as opposed to oppositional and judgemental, for example, which often happens when challenging people who are in a position to judge you/yours), you can state that she evinces a classic example of the Dunning-Kruger effect of being in possession of inappropriate confidence.
As the (Dunning) article states, we are all confident idiots. In Dunning's words,
In many cases, incompetence does not leave people disoriented, perplexed, or cautious. Instead, the incompetent are often blessed with an inappropriate confidence, buoyed by something that feels to them like knowledge.
Or, simply, she is over-confident.
Solution 3:
It sounds as though the social worker arrived at her conclusion after a superficial analysis based on a superficial examination and with relatively superficial knowledge of the various ways OCD can manifest itself depending on the child and on the conditions of the exam. In contrast, your doctors made their diagnoses after thorough analyses of their thorough examinations and a broad and deep knowledge base of many children with OCD.
Superficial, from The Oxford English Dictionary
Not thorough, detailed, or complete; cursory ............
2004 Plain Dealer (Cleveland, Ohio) (Nexis) 3 Oct. c20 Today, in an age of specialization, few people have more than superficial ability in two fields
...........
1945 H. A. Larrabee Reliable Knowl. ii. 76 Flights of fancy based upon superficial analogies and whims have misled millions for centuries
I suggest that you do not call the social worker herself superficial, or even explicitly call her training superficial, just the examination she made and her analysis of her examination, unless you are certain that you will never need her good will and you are certain that the people sitting in judgment of the case will not close ranks to protect one of their own.
I suggest something like:
Ms. Johnson arrived at an erroneous conclusion based on the necessarily superficial examination she was able to make with the time constraints and other constraints under which she was working.
Note that everyone answering your question is accepting your view of the situation based on only a superficial understanding of what is going on. (But it rings true.)
Solution 4:
Some ideas: smart aleck, braggart, walking encyclopedia, bragging (one's knowledge), disdainful (of other's knowledge), haughty, presumptuous, proud, puffed up, etc.
It is also possible to use formulas like he/she believes that he/she has the monopoly of the truth. Look for synonyms for "arrogant" or "immodest".
Solution 5:
A pedant is
a person who is excessively concerned with minor details and rules or with displaying academic learning." (NOAD)
The pedant's excessive concern indicates the same arrogance, as well as annoyance, as know-it-all. There is, of course, the adjective form, pedantic, and the excessive concern itself, pedantry.
(A pedant, though, like a know-it-all, might actually know what they are talking about, so it might not fit the situation you describe—but then I would argue that know-it-all might not either.)
Beyond the answer:
Thesaurus.com just taught me the gendered synonym bluestocking:
a woman with considerable scholarly, literary, or intellectual ability or interest."
I don't believe this word, though, carries the connotations of excess, arrogance or annoyance. It would not fit the situation you describe, or at least not achieve the ends you seek.