Sorry that I didn't reply sooner, I've been doing some research.
Another issue is my landlord does not allow pets, but I think they would take a service dog more seriously than an ESA
From the landlord's perspective, they're going to be worried about damage to the apartment from chewing and scratching, especially if it's a furnished apartment. Odors and stains caused by animals are another issue. Animals can also bring in fleas, or cause fires by knocking over candles, etc.
Landlords will also be worried about complaints from neighbors, particularly if they're are also tenants of the same landlord who might be driven off.
The biggest concern is if the animal is dangerous, but excessive barking is the most likely problem.
You can make a request under the Fair Housing Act for an emotional support animal. It looks like you'd have as much legal protection for an ESA as you would for a service dog, at least as far as housing goes.
Once you figure out what kind of ESA you want, you may want to talk to the landlord. If the animal you request wouldn't be too much of a burden, the landlord may decide not to resist. It's probably best to follow up any request with a formal request in writing, with a copy of a letter from a mental health professional supporting your ESA request (a MH professional may already know the format requirements for such a letter, but it may be helpful to reveiw those requirements to ensure that the MH provider observes them). The request should be signed and dated. Sending it via certified mail, return receipt requested, may help you to establish when you sent the request. Keeping a copy of all documents could help too.
There are some grounds for a landlord to deny a request, like safety or unreasonable costs, but it looks like generally they would be obligated to make an accommodation, and to also waive any pet-related fees or deposits, as an ESA is not a pet as far as the law is concerned.
If your request is denied, you can file a complaint with the FHEO. You may also be able to take other legal actions.
Information from the HUD's website that I have linked below may be helpful, and I'd recommend reading the PDF file titled "Notice FHEO-2020-01: Assessing a Person’s Request to Have an Animal as a Reasonable Accommodation Under the Fair Housing Act (January 28, 2020)" which is linked at the bottom of that page.
https://www.hud.gov/program_offices/fair_housing_equal_opp/assistance_animals
Here are a few excerpts from the PDF file that may be particularly notable:
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The Fair Housing Act (FHA) makes it unlawful for a housing provider to refuse to make a reasonable accommodation that a person with a disability may need in order to have equal opportunity to enjoy and use a dwelling. One common request housing providers receive is for a reasonable accommodation to providers’ pet or no animal policies so that individuals with disabilities are permitted to use assistance animals in housing, including public and common use areas.
Assistance animals are not pets.They are animals that do work, perform tasks, assist, and/or provide therapeutic emotional support for individuals with disabilities. There are two types of assistance animals: (1) service animals, and (2) other animals that do work, perform tasks, provide assistance, and/or provide therapeutic emotional support for individuals with disabilities (referred to in this guidance as a “support animal”).
An animal that does not qualify as a service animal or other type of assistance animal is a pet for purposes of the FHA and may be treated as a pet for purposes of the lease and the housing provider’s rules and policies. A housing provider may exclude or charge a fee or deposit for pets in its discretion and subject to local law but not for service animals or other assistance animals.
While it is not necessary to submit a written request or to use the words “reasonable accommodation,” “assistance animal,” or any other special words to request a reasonable accommodation under the FHA, persons making a request are encouraged to do so in order to avoid miscommunication. Persons with disabilities may also want to keep a copy of their reasonable accommodation requests and supporting documentation in case there is a later dispute about when or whether a reasonable accommodation request was made. Likewise, housing providers may find
it helpful to have a consistently maintained list of reasonable accommodation requests.
A resident may request a reasonable accommodation either before or after acquiring the assistance animal. An accommodation also may be requested after a housing provider seeks to terminate the resident’s lease or tenancy because of the animal’s presence, although such timing may create an inference against good faith on the part of the person seeking a reasonable accommodation. However, under the FHA, a person with a disability may make a reasonable accommodation request at any time, and the housing provider must consider the reasonable accommodation request even if the resident made the request after bringing the animal into the housing.