It's like a break up - it sucks right now, but you'll get over it. I have just got into a Grad program 7 years after initially finishing my undergraduate degree (I didn't spend every year applying - I applied once before in Philosophy, and the failure combined with life experience gave me the perspective to switch to Cognitive Science). Not getting into grad school straight out of undergrad is nowhere near the end of the road, and there are many valuable experiences you can acquire that will make you into an even better candidate in the mean time - whether it's doing RA work, or getting relevant work experience in another setting.
Also, take the time this year to look at the schools you could go to, and which ones you would really be happy to attend. It is fine to be picky about applying to particular schools, as long as you end up with a list of schools that you would want to attend if you got an offer from them, independent of whatever offers you received from elsewhere. If doing graduate work is massively important to you, would you be satisfied with attending a less prestigious program in order to do so? These are the questions that you have to ask yourself over the next year.
It does suck to be rejected, but at least it was only from two - I got rejected from 11 schools on my first Grad application round and that stung like hell (Philosophy admission stats are ludicrous).
You have plenty of options going forward, and definitely worth asking at your current institution if they know of any RA positions available after graduation. Good luck, and I'm sure you'll have better luck in another round of application.