Denis, my understanding is that getting into Mexico from the US side is fairly easy and straightforward. Like John mentioned, just be aware that there probably will be the usual crowd of people past the border trying to get your attention to exchange money, buy stuff etc, so just be extra careful with your stuff.
this does touch on the whole traveling on your own thing, its harder to keep an eye on your bike and belongings when its just you, so as a general message, be extra careful of not leaving your bike alone-at stores, border situations, carrying things up stairs etc.
Oh, nearly all motels, hotels are ok with you bringing your bike into the room with you, not all, so just be prepared to make a judgement call on if you feel ok leaving it in a given spot if the owners really insist on you storing it somewhere else overnight. I always have a coil lock to at least attach it to something, or through the wheels, but really, every situation is different.
were you thinking of bringing just rear panniers?
I would suggest bringing your sleeping bag, it can be very handy if its a cold room, or even if the sheets are kind of sketchy. I took mine even on the trip that I didnt take my tent, and used it in hotels often. Its a summer bag, so not overly bulky nor heavy.
your bike is already in Texas, but I hope that it is in very good mechanical condition and the tires in good shape. Bicycle shops are common, but you should start with very good tires that are rather new. Also, bring at least a couple of spare tubes, patches, glue (more than one tube of glue).