Perhaps a therapist, psychiatrist/psychologist and/or medication for yourself, not home remedies such as cooking oil on the dogs skin, that may have exacerbated any condition he may have. Yes, you can get scabies from a dog, as well as many other zoonotic health issues.
Definitely turn the dog into a shelter/rescue where he will get the care he needs, possibly be adopted by someone that Really Cares and has the experience/knowledge on how to care for a dog properly and don't get another dog. Pit bull is two words by the way.
Entirely up to you if choose to seek medical care for yourself, just as there are no veterinarians on this site there are no physicians either, neither of which can examine you or the dog on line.
All dogs need a lot more than that,they're not lawn ornaments to be left outside without supervision,they need a person to provide walk/elimination times,consistently on a daily set schedule,regardless of weather conditions and other daily constraints in your life.as well as daily aerobic exercise,such as playing fetch,mental stimulation,such as obedience training.They will not do this on their own in your yard, hopefully it's securely fenced in, most will just lie in the sun unless you go out there and work with it.Obviously with an infant and a one year old you may not have the time, he may have picked up additional health issues in the park as well.