Sure, you could create your own streaming system, but it will likely be cheaper in the long run to use a streaming service. I have no experience with any of these services, but a quick search on Internet Radio Services will provide you with several services you can check out.
The thing that you did not mention is how you are paying for the services (just your local advertisers?), and how you are going to keep track of songs played and how many Internet listeners were tuned in so you can stay legal with the song royalties. A service can keep track of those details for you if you wish.