First of all, congrats for kicking all the rest of the vices, since, I guess the rest were even more destructive than these 2. I'll be honest, kicking both is not easy at all and just like others have suggested, I too suggest to cut 1, not quit both at the same time, which will potentially leave you messed up for weeks on end, it is very subjective from person to person for how long you'll feel miserable.
Of course, quitting cold turkey can work if you can thug it out long enough for withdrawal/sides to fade to an acceptable level; for some people it is too hard on their body/mind, then they need some accessory medication for these 1-3 weeks after stopping. It can be pregabalin (albeit, in a controlled dosage), it can be supplements (in form of B/C vitamins).
I'll tell you this though, be very attentive regarding these things, because once you start to feel somewhat better, it is very easy to slip back into addiction downward spiral, like I've done countless of times with different substances. Be mindful of people around you too, since many of us, addicts, like to find other, likeminded people and usually not everyone wants/can quit at the same time..
I would say the toughest will be what do you do once you are free of substances and relatively recovered? Because if you was using for extended periods of time, you probably have surrounded yourself with people who use.. You probably enjoy plenty of activities being high as well. I suggest thinking about how you will handle all that, because life goes on and you need a good strategy to maintain your newfound sobriety.
Best of wishes and I'm glad you're trying.