Hi and welcome to the forum. Nice to have you with us.

Yes, if you have to rock your hips/legs side to side, your saddle height is definitely too high. Could be a cause of your problem, but, for sure, will definitely be a source of other problems, too. For instance, too high and you will not be getting max power with your pedaling. I like my saddle height to be where I can just touch the ground with the balls of both of my feet when at a stop. For my MTB riding, I sometimes drop just a touch lower, even. This really is a critical measurement, enough so that even changing shoes can affect it.

Be sure to check the tilt angle on your saddle, too. I spend a lot of time on this one, but it';s worth it. Too much tilt down in front will cause your skin to stretch in the sensitive areas and you won't get enough leverage off the seat to work your legs at the best. Too much tilt back will cause too much contact with the sensitive areas, especially when the road is a bit rough and bumpy. Again, really does have to be just right. Seat adjustments are one reason why I always carry a bike wrench.

Once thing that might be worth a try is using one a saddle from your MTB if still have one. No law says you absolutely must use a road saddle, but, again, I think how it's adjusted is the important thing.

As for width, Sheila is so right about getting that one right. Just remember, though, too narrow is also going to cause a lot of issues. I have a wide sit bone measurement, so narrow guy size saddles have always been a nightmare for me. Usually the first thing to go when I buy a unisex bike.