The octane content of the fuel controls the burn rate. The higher the octane content, the SLOWER the burn rate, so no...higher octane fuel won't hurt your engine, but it might hurt your ETs if it burns too slowly for the engine design or spark advance settings being used.
Lower octane fuel might hurt your engine. At some point, you reach critical temperature and pressure for the given octane and the fuel becomes an explosive rather than a propellant. Spark advance changes the peak pressure the cylinder achieves; retarding the spark ends up creating less cylinder pressure and is how most people avoid detonation.
A couple of deg of spark below where the mixture detonates is usually peak power. If the total advance value gets too small, the engine gets inefficient and will benefit from more octane and more spark advance. For example, if you try to run 87 octane on an 11:1 engine, your total advance will probably end up under 20deg. In that case, you're much better off running more octane so you can increase the advance and get the combustion event into an area of the engine geometry where it will make the most power.
So the real question is...how much advance can you run now before you start seeing signs of detonation? That will give us some indication of whether or not more octane might be of benefit, or is simply a waste of money and effort.