First off, I am an agent...and you need not be intimidated using me or anyone other agents in finding a home! That is our job, that is what we do!! Plus, when using an agent, our commission is paid by the seller/lessor, NOT by the buyer/lessee. So our services would be "free" for you...
Second, congrats on the baby! Hope you are enjoying the new addition to your family, and getting enough sleep.
Third, to answer your question, it looks like the rental price you are seeking is below market for these two specific zip codes. My search only looked up the listings on the MLS, so you may have a better chance of finding something in your price range if you drive and scout the neighborhoods, looking for "For Rent" signs. It will take more effort on your part, but can save you money in the long run, and keep you within your budget.
If you do decide to expand your search criteria, either by zip code or price, feel free to contact me - I will set you up so the listings come to you!
Alan Kurpiewski, RealtorÂ®
CA BRE 01912043