@Tatiana Conta Real estate agents have loyalties (which are great) to their lenders, and they don't usally shop for what is best for the borrower.
Yes, Brokers do shop for you. Make sure you explain what you want and what you want to do with the property. I will assume being on here it may be for investment. What is the plan for the property, Rental, Flip, house hack what ever yor plan is let him know.
The broker will then shop and (if good) will give you options and let you decide. During the process you will fill out an application, give him/ her information regarding assests, bank info and then will pull your credit score. That score will be active for 30 days and if someone else pulls its during that time, it won't affect your score. So that being said, you can even shop brokers. all brokers have access to more or less the same lenders, some local lenders being the exception.
Just like your agents it's all about relationship created with you and the personality and way of working that makes its a good fit. I hope this answered your question. End of the day you don't have to stay with the broker if you don't get along with them. I've had some hit or miss with real estate agent and some of them I won 't work with again, unless they bring me money.
Hope this helped
Sergio