Lip lift revision 1 month after initial procedure - should I be concerned about necrosis?

I had a lip lift done 1 month ago in Korea, after a rhinoplasty the month before. As the surgeons were conservative with the lip lift, I am planning a revision to lift another ~3 mm. The hospital declined the revision, saying there was a risk of necrosis from damaging microvessels in the philtrum, esp. given the recent rhinoplasty. I consulted with another reputable Korean hospital, which agreed to go forward with the revision. Should I be concerned about the risk of necrosis? Thank you.