If you don't believe in God where do you get the strength to cope?
I actually would take exception to the question itself, Miss.Fit. There's no need to "get" strength from anywhere. All living things that are healthy want to continue living; their "strength" is in their continued biochemical reactions that constitute their life processes. Only when an organism is heavily damaged does it want to end its suffering. But as long as you live healthily, you will naturally feel strength within yourself, and want to live; the exception to this is if you are indeed suffering from a chemical imbalance. You might need meds for that temporarily, but a lot of people are able to go off meds once they find out what's harming them mentally or physically. Obviously if you're not getting enough sleep, that's going to sabotage everything in your life. Eating right, obviously... exercising is a must because our bodies are supposed to be active throughout the day. It could be that you're simply not putting your own mental and physical health high enough on your list of priorities. When was your last vacation, your last do-nothing day?
One big thing that separates humans from other animals is that, because we can contemplate the future, we can envision our own deaths, and this can be a heavy thing to deal with, to be aware of our own mortality. There are lots of ways you can deal with this. There are many people who do not believe in an afterlife and yet are unafraid of dying. Personally, I view myself as part of a continuum of life. I'll accomplish what I can with whatever time is allotted for me, and then I'll pass my resources back to the planet to be used again in some other life. We're already made up of many people who died before us. I don't place a lot of emphasis on myself, but then again, my philosophy is not for everyone as it requires solitude and detachedness.
Many secular-minded people simply focus on their loved ones, as some have indicated in this thread. They make themselves about the other person or persons, and this brings them inner contentment (this seems to be more natural for women than men). Some who don't believe in God still believe in some sort of cosmic force like karma or reincarnation which gives them some peace of mind because they can believe in a universal sort of justice. Some people may not believe in anything supernatural, but they set aside time each day to meditate. Meditating can give you the same benefits as praying (since, if God is not listening to our prayers, what is prayer but simply meditation on what we need and what we are trying to do better at?).
But, in my non-professional opinion, you're mainly just feeling temporarily shocked at the change in your beliefs, and possibly you are over-extending yourself on behalf of others or going too hard on yourself physically. Keep in mind -- no matter what you believe, life goes on. Our inner beliefs can't change the direction of a single falling leaf or cause a single ripple in a puddle. If you've made it this far believing there's a God when really there isn't one, then that simply means you made it this far entirely on your own strength and with the support of other people! Thus, there's no reason to be too worried about having "the right beliefs". Life is about enduring, finding a purpose to work at, and hopefully having some fun along the way.