IMHO, doms doesn't mean you're growing, though it can signify a workout that will lead to growth.
If you have DOMS PWO, chances are you ARE growing. If you don't have DOMS PWO, it doesn't mean you're NOT growing.
However, ANY new activity will cause DOMS, regardless of how well it's performed or how useful it is. Go work on your car for a day. You'll get DOMS pains in all the muscles you used to hold eccentric positions... Though you likely won't end up with any growth from it. Inside a workout context, getting DOMS is a fairly good indicator that you've worked out properly, though it is not - and should never be - considered anything but one sign of many.
As for dealing with it... Well, don't take a hot shower right after a hard WO. Heat = swelling = more local trauma. Sleep and food can jumpstart the repair process and really help deal with DOMS. I used to get such bad chest DOMS (from flies) that I'd tear up with headaches. An extra 500kcal from good protein food, and a good 10 hour sleep almost always mitigated the pain. Hot baths the day after, to increase blood flow and recovery help too. Fascia stretching is the ultimate DOMS buster, if done before a good sleep (after a good meal, of course). Finally, if your DOMS is lasting more than 2 days, some light cardio near the end of the 2nd day will stimulate blood flow, and help repair muscles too. Oh, and a bit of cardio post lifting workout, around 10m of jogging after a 5m walk or so, seems to help a bit.
Whatever you do, don't take analgesics (unless you can find/buy some OTC opiates) as they halt protein synthesis greatly.