Hey, start by taking a deep breath. You are not alone and it's not wrong to feel like you are mourning a loss because that is exactly what you are doing. Each break-up is different whether good or bad and you have to allow yourself to process whatever feelings and emotions may come your way. I ended one relationship that was so toxic my friends practically threw me a party. The more recent break-up has had me feeling crushed. No two experiences are identical. But I've learned a few things along the way that might help you...
Start by allowing yourself some time to grieve. You may be feeling like you lost your best friend, your confidant, your lover, and many other things. The feelings of sadness, being emotionally lost, feeling despair, and hurt are all signs of grief. You mentioned that it's been around 3 weeks. It's still relatively new but there will come a day when you have to end the grieving process (more on that later). Embrace the pain and let it move through you, don't let is stay stagnant.
Next, find a distraction. Whether it's refocusing your energy into a hobby, other friends, work, or even a video game - you'll need something to help kill time. Otherwise, you'll continue this mental roller coaster of high highs and very low lows. Right now your state of mind is incredibly volatile and impressionable. That chair in the corner where she use to sit and read her book? The mug she always had her morning coffee in? The way she would smile and laugh at your jokes? The corner shop you use to stop in for brunch on the weekends? All of those are triggers. Hell, I watched a commercial last night that damn near made me want to cry because some trivial reminded me of my recent ex. This is why right now, in this phase, you must MUST MUST find a distraction.
Then you have to physically leave your house. Don't allow yourself to be a shut in and perpetually lost in grief. Go sit on your friends couch and hang out but with the rule that there is no talking about your ex. The point of this exercise is to mentally retrain yourself that the topic of your ex is no longer available. When you reach this phase, it requires a lot of action on your part. Your good friends will wan to be there to help you along. Find them. Be around them. But know that forever being the "guy who just broke up" will drive away friends faster then anything else. When people first hear about the break up, be succinct. And for the love of all that is holy, don't be a Ted Mosby. Constantly whining about the love you lost is the worst thing you can do to your friends. Grieve, share as appropriate but actively work to retrain your mind to move on. When those triggers pop up, when those moments hit you -- remind yourself that there were good times but for whatever reason it didn't work out and it's time to move on. In no way shape or form is this an easy task, but it's incredibly important to your health.
The last big hurdle to face when dealing with a break up is knowing the fine line between appropriate greiving and feeling sorry for yourself. The former is 1,000% acceptable while the later will alienate you from friends, family, and those who want to see you happy. I suggested taking time to emotionally grieve the loss of your friend, companion, lover, confidant. Do that. But don't let it consume you. My g/f of a year and half ended things with me less then 2 weeks ago. I was ready to buy a ring when she confessed that she didn't see a future with me. I was crushed and still am. I share all of this with you out of empathy and love, internet stranger. There will be better days ahead even if it doesn't seem like it right now.
Yes, there will definitely be times when you miss her. When you want to call and share a funny story or just tell her that you are excited to see her. But those moments can no longer exist in your world going forward. This is where you have the toughest fight ahead of yourself. Retrain your thinking process to know that you are perfectly fine without your ex. The distractions can certainly help you regain a sense of self to know that you world doesn't start and stop with another person. It starts and stops with you.
TL;DR Steps to recovering from a break-up: Grieve, find a distraction, go out, retrain your brain, your word is YOURS.