According to your description, looks like you just want the URL of created WorkItem, so that anyone when click on URL, created Work Item will be Open.
https://tfsurl:8080/tfs/DefaultCollection/PatrickProject/_workitems/edit/172/
The URL should be above format and here DefaultCollection is the collection name and the PatrickProject is the project name. I used this url and got rid of the id '172' in this case and use the ID of newly created work item. This would return the URL to go to the work item HTML page.
So it's a fixed format, if you have Newly Created WorkItem ID and collection name , project name, you just need to follow above format and change the last value of work item ID. That's it , ignore of which work item type you created.
If you want do this with code, do not use Rest API, you need to use client API, sample snippet:
var tfsURI = new Uri("http://test:8080/tfs");
var networkCredential1 = new NetworkCredential("test", "test!");
ICredentials credential = (ICredentials)networkCredential1;
Microsoft.VisualStudio.Services.Common.WindowsCredential winCred = new Microsoft.VisualStudio.Services.Common.WindowsCredential(credential);
VssCredentials vssCredentials = new VssCredentials(winCred);
using (TfsTeamProjectCollection collection = new TfsTeamProjectCollection(tfsURI, vssCredentials))
{
collection.EnsureAuthenticated();
TswaClientHyperlinkService hyperlinkService =
collection.GetService<TswaClientHyperlinkService>();
String TFSurl = hyperlinkService.GetWorkItemEditorUrl(17648).ToString(); //17648 WorkItem ID
}
Hope this Helps!