Call your local welfare office, explain your situation to them. They should have a list of local shelters you can go to. If that doesnt help, then call your local housing authority and find out if they have any vouchers that can help you get an apartment. Sometimes, housing authorities have their own vouchers that some landlords will work with.
Sorry to say but in this day in age, people ask for proof. About 9 years ago I lived in that neighborhood and we loved the neighborhood. My daughter had a high school friend whose family lived at the Meadows. There are several pictures of the exterior but I did not see pictures of the interiors. My impressions of them years ago was that they were pretty ordinary, nothing special but okay. This site gives information of prices and floorplans as well. It tells that the apartments are owned and managed by AIMCO which is a huge Real Estate Investment Trust operating nationally. They own many other properties in Austin too. They had great floorplans but also were nothing great. The Meadows and the others in the immediate area were probably 30 years old, they may have had a remodeling by now but I do not know.
The reason that I took the job at Westwood was that it was directly across from Westwood High School and I had a 9th grader at the time. Also next door was Audobon Square which had exactly the same floor plans but was more updated at that time.
Both of these were a little more interesting than the Meadows. The Meadows was: okay, beige, not much color, quiet, reasonably priced.
It probably still fits that description. If you are looking for an apartment, a good way to find one is to call a locator. The apartment complex pays their fees. You tell them the area you want, the amenities that you want and the price you are willing to pay. They can fill you in on everything. They will either direct you to the places that have openings, or take you there themselves, depending upon what arrangements they have with the complexes.
Good luck in Anderson Mill area. We loved the HEB down the street. My daughter and her friends were 14, could not drive yet, but could walk all over the neighborhood. It has grown like crazy since we lived out there but it is a great area.