Setting the storage engine to InnoDB will indeed help with performance. However, it may not be the end all bullet. You will want to talk to your hosting provider about changing your tables for you to InnoDB.
I would also recommend disabling any third party applications/plugins and switching to an unmodified theme when evaluating performance. This will allow you to set a baseline for your performance on the core software and then evaluate the third party add-ons on top of it one-by-one. It could be one of these third party add-ons is not performing well on your server or is expectedly doing something that is a little more resource heavy.
If none of the above helps, you will want to re-evaluate performance with your hosting provider with all third party items disabled. If the hosting provider finds something very specific which is a software error or slow query. We would require the proper logging to diagnose. However, generally, performance issues typically lie on the hosting side of things and they have the tools/resources to help you resolve them.