Yes, you may.
http://www.txdps.state.tx.us/interne...rms/chl-16.pdf
As far as a hotel safe, why use one, carry it. If you have to go into a school, lock it in your trunk. I don't support that, but the law does not permit the carry on school property, without written permission from that ISD. So what else can you do? If you leave it at the hotel and have a flat halfway across town after you miss your exit and wind up in south Dallas at night that gun is no help at all in a hotel safe.