If I understand correctly, you need to give access to the web service only for authenticated users.
There are many ways to secure a web service. Since you are using AuthenticationAdmin to login, you can define your web service as an Admin Service.
I guess you are trying code first approach for your web service. You can try extending your web service to org.wso2.carbon.core.AbstractAdmin.
For example, we can see UserAdmin service in WSO2 Kernel. https://svn.wso2.org/repos/wso2/carbon/kernel/branches/4.1.0/core/org.wso2.carbon.user.mgt/4.1.0/
UserAdmin service: https://svn.wso2.org/repos/wso2/carbon/kernel/branches/4.1.0/core/org.wso2.carbon.user.mgt/4.1.0/src/main/java/org/wso2/carbon/user/mgt/UserAdmin.java
axis2 services.xml: https://svn.wso2.org/repos/wso2/carbon/kernel/branches/4.1.0/core/org.wso2.carbon.user.mgt/4.1.0/src/main/resources/META-INF/services.xml
You can see following properties in services.xml
<parameter name="adminService" locked="false">true</parameter>
<parameter name="hiddenService" locked="false">true</parameter>
Using the generated WSDL from this service you can create the service stub.
Now you can use the stub and your cookie to access the service. For example see https://svn.wso2.org/repos/wso2/carbon/kernel/branches/4.1.0/core/org.wso2.carbon.user.mgt.ui/4.1.0/src/main/java/org/wso2/carbon/user/mgt/ui/UserAdminClient.java
ServiceClient client = stub._getServiceClient();
Options option = client.getOptions();
option.setManageSession(true);
option.setProperty(org.apache.axis2.transport.http.HTTPConstants.COOKIE_STRING, cookie);
I hope this helps.
Thanks!