Depending on the kind of noise, the proximity of the noise source, and the sensitivity of your hearing, earplugs are sometimes not strong enough to block out the noise completely or even sufficiently.
Do you have the ones that have to be rolled into a ball? They must be spread across the opening to your ear so that they cover it completely. If you used them correctly with unsatisfactory results, you may want to try using more than one tool at once, for example, earplugs and ear defenders simultaneously.