Could my dog have worms?

Im a first time dog owner and i have a question could my black lab puppy who is currently 7 month old possibly have worms? She has to been to here vet and has gotten the vaccination against worms and about 4 months ago has had a test to determine whethere she has them or not. It came out negative, so she did not have them. Today though, i noticed two worm-like creatures on her tail a bit above her butt. I looked around her anus but found no worms. I also looked in her fresh( as in 2 minutes after pooping) stool and also did not find worms.I will check again tonight. It does not seem that she has butt irration but she thrown up this week on tuesday and lastsaturday. But both days we could find something she ate to blaim the throwing upon. For example, on tuesday she accidently ate some of my clay pot. So, with all these infro could it still be possible that my dog has worms. Im really scared. I heard a dog could die from worms. I dont how i would surive without my dog! Were sooo close! and i fricken love her to death. I love my dog more thanmy sister. Please answer my question!PLZ!!!!! The only reason i have to think she has worms is because i found two worm-like creatures on her tail. They were whiteish color a bit tannish too and moved. Idk!! I told my mom and she said that she doesnt think she has worms but that it could possibly be from outside because she had just come from our yard. P.S she had been laying on the patio bricks! Idk! Shoudl i take her to the vet? My mom said that if we have to take our pup to the vet we will but if dont really have to we shouldnt because right know were kinda low on money! PLZ!!!" HELP! PLZ NO RUDE COMMENTST! Thanks