The depressor septi nasi (DSN) does contribute to support of the upper lip as you pointed out, but there are other factors involved as well. If the DSN is truly and fully cut, it is unlikely to regenerate. I stay away from this and prefer to release select sections of the muscle from the tip structures to achieve the desired nasal result, while avoiding the negative lip result. I also find it more important to support the tip itself rather than to weaken the musculature of the nasal base and mouth. Sometimes there is swelling and weakness of the muscle immediately after surgery, and this usually lasts for approx 1-4 weeks.There many also be transient injury to the levator alaeque nasi muscle. It would be unlikely for this to be fully cut with rhinoplasty. It could take 6 weeks - 3 months for this to come back. Try some facial exercises, uses a mirror, elevate the top lip as you would like to see it but with facial muscles only. Like physical therapy for the face. It's worth a try. If this issue persists and doesn't resolve, a lip lift can help ... but make sure it's done properly with good deep support, which will support the obicularis muscle. Amount of time to wait is at least 3 months, but 6 would be better to allow full healing and resolution of swelling in the nasal base. Hope that helps!