It's an interesting question, and one that bothered me for a while!
Although some people frown on it, my council was persuaded to reinstate an old traditional agenda item "Questions to the Chairman". Under this item it is unlawful to make significant decisions, especially about expenditure, because as an agenda item it doesn't say what business it will cover. But it does allow councillors to raise new matters or stop old matters from sinking into oblivion.
Another factor is that councillors are able to put forward items for the agenda, and there are only limited reasons for excluding them from the agenda. So usually a councillor should have the power to bring up a matter on the agenda.
If all else fails, I can't think of any reason why a councillor can't take advantage of the public session. Although it might be more effective to brief a friend or relative to raise questions.