If you want to look at new bikes, I noticed the other day that my LBS (in Reston, VA) has some from last year on sale. They're a Trek shop, not Specialized. Other shops closer to you might also have some of last year's bikes on sale, and they should all have some at the end of the summer when the 2016s come out, if you want to wait. They also tend to have sales in July to coincide withe Tour de France.
As for whether you need a new bike... I did not really get faster when I upgraded from an aluminum road bike to a carbon frame. My new bike is much more comfortable, though, due to different geometry as well as carbon's ability to absorb bumps in the road.
One thing you might want to consider is new wheels. There are various old threads here you can search for. I think a wheel upgrade might make a difference, and they could also be used on a new bike if you decide to get another one in the future. I could ask my friends in southern MD if they can recommend a good wheel maker, if you're interested. I know there's a good on at Spokes, etc., I think at their store on Quaker Lane in Alexandria.
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles