It was actually quite a journey finding the right one. There's a whole slew of non-SLS toothpaste out there but 99% seem to decide they should remove fluoride too.
I eventually found Trader Joe's had a fluoride anticavity toothpaste with no SLS. Another benefit is it doesn't contain any sweeteners, which was odd when I first tried it as almost all mass-market toothpaste is highly artifically sweetened. It's really pleasant to use and affordable too.
I went ahead and found it on Amazon in case you don't live near a Trader Joe's. It's cheaper in store though so worth a visit if you live near one.
I'd stopped using sulfates skin or haircare, but I still had those chin whiteheads. Switched to sulfate-free toothpaste (Trader Joe's Anti-cavity Peppermint) and the whiteheads on my chin went away. I still have the occasional breakout, but those chin guys are long gone.
Switch to toothpaste that doesn't contain sodium laurel sulfate (SLS). It helped me out a ton when I started using Trader Joes natural toothpaste.
Trader Joe's All Natural Anticavity Peppermint Toothpaste with Baking Soda and Fluoride 6oz (Pack of 2) https://www.amazon.com/dp/B008MG5QPI/ref=cm_sw_r_cp_awd_IjGkxb3YRW09F