hmm it shouldn't take too long I think! I went to the polyclinic and got a referral to KKH. The doctor said KKH will call me within 2-3 weeks but I got a call the day after and my appointment was a week after. There were many slots too! So I could reschedule to any timeslot within the week. You can try calling NUH?
If you’ve gotten a referral, you should just download the health hub / nuhs app to check by signing in your singpass. They will update the appt date faster there!
just call them cos I put in an appt via nuhs app and it took 1 week ish and no reply.