Should I send him a relationship request on facebook?

[Jericho]

No, I don't suggest you going ahead and sending him a request... I've had my own experience with this (gender reversed) and it didn't go to well... you shouldn't really need to fret over this, but if you feel this is significantly important enough to you to make this go ahead, you should always (ALWAYS) make sure this is okay with your significant other. Talk to him, ask him, be clear about it; and that it means a lot to you and he may say yes.

So first off think about how important it means for you to have this "symbolic" gesture, as in our day of internet, many things; "labels" can seemingly look life changing while in fact, when you take a big step back and think... it might then again seem trivial.

Patience and time prevails
Love is timeless and it is patient, for without patience, time is loveless.

Best of luck to you, and hope you make the right decision for both of you, and enjoy love for what it is.