Should I go to the doctor because of my dog?

I got a new dog that was neglected a bit he had sores on his body in little spots with missing hair not a lot and his skin was super dry and flaky he also had worms. I treated him for it all and put Cooking oil on his skin twice daily it's been 3 days his skin is healing the worm treatment is over and his skin... show more I got a new dog that was neglected a bit he had sores on his body in little spots with missing hair not a lot and his skin was super dry and flaky he also had worms. I treated him for it all and put Cooking oil on his skin twice daily it's been 3 days his skin is healing the worm treatment is over and his skin isn't flaky anymore but he does have the little red patches in his skin and he licks himself every now and then. My dad said it was mange and that you can't get it from dogs but I heard otherwise that humans could get scabies from dogs which is gross and not good at all I'm wondering if I should just give him away because there is baby's in my house and I don't want him to get them sick I've been keeping him outside in a big dog house and the yard for the most part he is a German shepherd pitbull mix and is barely over a year old. I've been washing my hands and my clothes after being with him but I'm starting to feel very itchy and uncomfortable I think it's because of reading that u can get scabies. Should I go to the doctor and check it out? I would want to catch it ahead of time cause there is a newborn baby and a 1yr old in my house as well as 6 adults
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