If I chose nexus and global entry can i do global entry now and do my nexus at my schedule appointment date (3 months)?
No. I called a Global Entry office specifically asking that and they said I need to go to the Nexus office.
To get an earlier appointments try:
A) Just walking in and convincing them to take you
B) Keep going online and click reschedule and see if anything else earlier opened up. The first avail appt will show up. Usually that will be a few months out, but if you check multiple times during the day, when someone say next week happens to cancel, all of the sudden that spot will be the next avail appointment but you have to be quick because anyone else who logs in will also see that as the first avail appt. I managed to get some family members earlier appointments by keeping that tab open in my browser and checking every once in a while. People do cancel/reschedule their appts, and if you are the next one to look for an apt you can grab it.