I am a certified relocation agent with Prudential California Realty. You may contact me, letting me know the details of your search. Neighborhood in LA you are looking into, single family home or apartment , and price range.
usually a Realtor gets paid a commission from the lanlord and it is free to you. However, everything is negotiable and if you want someone who help you in a complicated case, you may have to pay for their time.
You can try driving around and looking at "for rent" signs and then call directly and explain your situation to the landlord. They may require 2 or 3 months deposit.
I focus on high end residential and apartment buildings for sale, so I cannot help you, but someone else in this forum may be able to.
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Just ran a search for you. The MLS has 66 places for rent in West Hollywood. What price range are you looking at and how many months deposit can you pay upfront? Two weeks ago I helped someone in a similar situation find a place. I'm sure, given the chance, I could help you find a home too!