Can I go under general anesthesia again after a week?

It would be nice to find one surgeon who is good at doing both. A browlift is relatively quick, whereas a rhinoplasty can take several hours, depending on the surgeon and your situation. I would prefer to do the shorter procedure first (but the swelling from a browlift may interfere with the rhinoplasty).

The ability for a patient to undergo general anesthesia can depend on the patient's health.  You should speak to both anesthesiologists who would be providing your anesthesia for both the rhinoplasty and the brow lift.  They should be able to determine if there would be any concern with you having general anesthesia for two procedures a week apart.  If you are completely healthy, there most likely would not be any problem with having the two general anesthesias in two consecutive weeks.  

It would not be unreasonable to undergo general anesthesia on 2 separate occasions a week apart for brow lifting and rhinoplasty. however, it may be near best interest to see a specialist who can perform both procedures safely and simultaneously.  Best of luck to you!