Sex addiction treatment expenses deductibility

if they are, then it would be a medical deduction.

only the medical expenses that exceed 7.5% of your income are deductible and you must 'itemize' and not take the standard deduction for it to make a difference 

I'd refer you to IRS Publication 502 (linked below) to determine for yourself whether you wish to include this type of treatment as a qualified medical expense.  The publication DOES approve "psychiatric care" as a qualified medical expense deduction.  So if you're admitted for depression, as you mention in your question, you may be able to use these expenses.  The sexual addiction part is what isn't clear in the publication.  Additionally, as noted in the answer provided by @NCPERSON1 and @Hi Palms, you'll be allowed to deduct only the qualified medical expenses that EXCEED 10% of your 2019 AGI.  AND you'll need to itemize your deductions on Schedule A, as well.  So your expenses would need to be substantial in order for this deduction to prove beneficial.  Here's the link to that publication.

https://www.irs.gov/pub/irs-pdf/p502.pdf