Hello. Thank you for sharing your concern with me. As someone who once had several arguments with parents to get a dog, I understand how you feel. A pet can be a great family member, a friend, and a sibling. However, taking care of a living creature is very difficult and requires a lot of time and effort. All that small living thing can trust is “you,” and if you are not yet ready to take care of others, it might be a bit early to have a pet.
On top of that, if you want a fur animal, some family meetings might be necessary for your situation of having an allergic sister. I don’t mean that you shouldn’t get a dog or a cat! I lived with my aunt, who is allergic to dogs and cats. However, when we decided to have a pet dog, I promised to vacuum the house twice a day and not let the dog in the bedrooms. After all, there was no serious medical issue, and we lived together for six years. It might be a difficult process, but you might want to convince your parents by telling them the responsibilities you will have.
Lastly, I recommend having a small animal like a hamster or a hairless animal like a sphynx cat. If you're going to have a dog, I recommend a poodle. Unlike other breeds, their hairs don’t sprinkle all over the house but just get longer, meaning that you only have to trim them once in a while.
I hope you can convince your parents and have a new family member soon!