Just google "Houston RV Storage" - you should get a number of hits.
Most of the large storage places have RV parking spots available. You may have to call several to find one that has availability - but I bet you can find a spot this afternoon if you start calling. HOWEVER, they will want some type of proof of ownership and proof of insurance. If all fails, call the local Airstream dealer(s) and ask their help. They are located through Airstream.com search/dealers. Good luck from Texas, paula