The options for a career working with animals are many are varied, as are potential routes from an environmental science degree. While there is plenty of crossover between those two, there are some notable differences. Environmental scientists tend to focus more on toxicology, pollution issues, and the environmental issues that impact both human and wildlife health, and the discipline has a solid foundation in biochemistry. Working with animals can include veterinary science and service, agriculture, conservation biology, zoo and aquarium work, animal rescue and rehabilitation, pest control, and so on. One doesn't necessarily need a foundation in environmental science for any of those.
What I would suggest as a key next step is to explore internship and volunteer opportunities that give you a taste of what different sectors and professional roles involve - there are many opportunities out there in government agencies (federal, state and city), NGOs and non-profits, educational institutions, and private companies. Your academic advisors and career services should be able to help you identify and apply for anything that appeals to you. Now is a prime time to start looking ahead of the summer next year.