No, you should be fine. In general, a real estate office will have many agents, and one licensed broker. If one agent writes an offer on another agent's listing, then the broker would become a "dual agent", with each of the sales agents still representing their respective party (i.e. your agent represents you, and the listing agent still represents the seller). Best of luck in the offer!
Your agent has certain legal and binding duties to you as your representative. Primarily these are to obey your instructions within the confines of the law and to be loyal to your interests, placing them above all others in the negotiations of a transaction. I have found in my years of practicing real estate that most Realtors are very ethical and take these standards seriously. You should discuss with your Realtor your concerns but understand that he is advocating for you in this transaction and not his/her brokerage just as the sellers agent will be acting in behalf of his/her client and not the brokerage.
I work wonderfully with many agents at my company as well as other companies. I find that the agents at my company, however, have similar values, ideals and education history which create successful negotiation. So many time we view negotiation as how do I win and make the other party lose, when in actuality, the most success for both parties come in a win-win.