Yes, it is appropriate and normal for an agent with whom you have discussed purchasing a home and especially with one who has shown you homes to send you a "client portal" to the MLS which will give you the opportunity to search homes with your qualifications. As an earlier responders said, each is trying to earn your business.
Texas has the benefit of allowing and encouraging buyer's representation by establishing a special buyer's agency between the agent and the buyer. This representation is by means of a contract entered into between an agent and a buyer. Usually it is an exclusive agreement between the two parties. You will also receive a form called Information about Brokerage Services which attempts to explain the concept of "agency" on your first substantive contact with an agent. (A good buyer's agent will explain all of these terms and concepts to you.)
If you do not enter into a buyer's agency agreement with one realtor, any realtor with whom you are working is actually representing the seller and the seller's interests. Your buyer's agent will represent you only and not the seller.
Under normal circumstances in Texas, the seller pays the real estate commissions for both the listing agent and the buyer's agent in a transaction as part of their closing costs; however, this item is negotiable.
Buyer's representation is relatively new in the real estate business although it has been around for at least a decade in Texas. It's a good deal, and it protects your interests.