Is it possible to perform an SQL injection inside an XSS attack? And if so, where can I find information on this or some examples?
That depends on what you mean by "inside". For example, as Conor Mancone suggested, there could be a combined reflected XSS and SQL injection. That could look like this:
http://example.com/badendpoint?q=<script>$('input').value="';DELETE FROM USERS;--";$('form').submit()</script>
In this example, the SQL injection is the payload of the XSS. That's sort of putting the SQL injection "inside" the XSS.
As nobody said, it may be better to call this chaining the vulnerabilities together.