First off, relax.
There may be something to it, but as you are right to question, it could just be the NRE. I have had a similar experience and after the NRE wore off, I still have that strong feeling of connection but the need to be with him all the time has worn off.
If you are worried that you are neglecting your other relationships, talk to them. Find out what they think and feel. They may be very understanding that you are dealing with NRE or they may be hurt in which case you do need to take a step back and work on those relationships again with the knowledge that it can make your new relationship even better.