You need to define with high precision what it is that you exactly want.
Here, you want to allow accesses from you, personally. The business with the secret key means that access will be granted to whoever/whatever knows the secret key. Embedding the key in the application means that the application knows the key, not you; and, as you note, secrets embedded in a widely published application are not really secret.
So, you have to be clear with yourself. First of, define who should be granted access, and by "who" I mean "the humans". Every human in this set should "know" a secret value which is used by the server to authenticate the said human. If several humans use the same secret value, then the management of this secret becomes complex, because you cannot enforce forgetfulness: you cannot evict a user from the set of people who "know the secret" because he will remember it nonetheless.
Therefore, you should have user-specific secrets. Each human should have his own secret value, and send it to the server to be granted access (since we are talking about sending secrets over a network, I assume that all of this happens under the aegis of SSL). Then comes the question of how technically a user will store his secret value. If he stores it in his head, and make it available to the application he uses by typing it when required, then this secret is a password. But other models are possible, e.g. the secret could be a bunch of randomly generated bytes which the user stores in a file along his app.
You cannot prevent a user who has access to your server from "sharing" that access with anybody else; but with user-specific secrets you can at least:
- know on the server who is (allegedly) connecting, and thus modulate the set of operations which the server will allow or disallow;
- evict specific users, by removing the secret server-side, without impacting other users.
What you cannot do is to have an app that everybody in the world could download and install and use to access your server, while reliably preventing any access which did not use the exact app that you published. This would be the Holy Grail of piracy prevention, and it proves as elusive as its theological counterpart.