Can roundworms be passed through skin?

Ok so we have a little puppy and he appears to have small rice or noodley like worms in his feces. He has some diarrhea and he seems to burp or almost vomit but nothing comes up alot. We haven't treated him yet but I looked up some information online and it seems he has roundworms. They said they can be passed to humans by ingesting them and I just wanted to know if that's the only way they can enter human beings or can they go through the skin or any other body parts other then ingesting them? My body is crawling right now because I hate bugs or any type of parasite bug like thing. I feel sorry for the puppy but I also want to make sure my family is safe from getting these because they can cause serious damage mostly in children. So is the only way to get them by ingesting them? what all can I do to prevent this? I used gloves to clean the mess up after I noticed them in his poop. But the first time I just used paper towels and hadn't really cleaned up that well. Even if I or another family member were to get them, would it be severe. like something to really worry about? I heard they are mostly dangerous in children. please help.