Dont feel like I can grow in this HR role. Should I look for another even though I don't have much experience?

I work at a smallish company selling a product. I worked as the only customer service rep for a year. Late last year, my direct report suggested I take on some HR responsibilities and the company paid for me to get an HR certification. They don't have an HR dept.

I fucking love HR. I just started a degree program to earn my BA in HR management. This is my career path.

I currently split my time between customer service and HR. My workload is overwhelming now. I've requested to be fulltime HR and believe the company would benefit from this but it is hard to showcase how I can help when I am responsible for customer service related things (some not even in the CS job role when I started). Also, my direct report is the marketing & engagement director. She continually disallows me to take certain responsibilities that would normally fall under HR claiming they are 'engagement'.

HR is a very experience-based field. Many jobs want at least a few years. I have almost one and could continue to wait it out at my current job to be given a primarily HR role. I could, however, attempt to get my foot in the door with a company that has a more structured HR dept. and incorporates HR with administrative duties, for example. Aka... "better" experience??

1. Should I stay at my current company a little longer doing half-HRish things to get experience?
2. Start applying for jobs that are well defined and relate directly to HR, hoping my current experience and the fact I'm getting my degree could get me in?

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