If both sides look the same, you likely not having any unusual problem. It's common for one side to hurt more than the other. Nevertheless, my feeling is that if you have any concerns this soon after surgery, it's best to have your surgeon take a look. A lot depends on exactly what was done. If the bones were fractured, its possible that one can be displaced if the fracture was unstable. More than likely, everything is fine, but it's always best to check.
I'm hoping that your plastic surgeon took your splint off. You want to avoid manipulating your nose in the early healing. It does not take a lot of pressure in some situations to alter your final outcome. Pain and swelling is not always symmetrical. The fact that you have more swelling
Though you are 10 days out from surgery, your nose is still in the early stages of healing. The fact that one side is more sensitive doesn't point to a specific concern. Depending the preoperative shape of your nose and what maneuvers were performed, there is the possibility that more intervention was required on one side over the other. This may be particularly true if your nose was crooked and required straightening. It is unlikely that you shifted your nose with slight pressure applied, but for any postoperative concern is best to consult your surgeon sooner than later. Bone healing may take up to 6 weeks and during that time your nose will be more susceptible to external force. Take caution with manipulation, wearing glasses, etc. Again- would urge you to contact your surgeon. Hope this helps.