Is "mazelas" only used in old Portuguese?

No, it's used nowadays too. Virtually everyone knows its most common meaning, since the media, teachers and politicians have used too much the expression "mazelas sociais". So, if someone eventually says "mazela", the listener automatically thinks "social".
Therefore, this sense would be regarded as a undesirable cliché within more formal contexts.

Besides this, the other meanings have semi-cult or cult essences today.
You can still use some informally in more cult groups, even of young people, however.

But, nevertheless, hardly someone would understand you perfectly if said as in your example. People mainly think of 'a problem, a issue; something bad' and not of an annoyance. It's not the case for its derivatives, like 'mazelar', but this is too cult, it has great restrictions.