You're better off avoiding labels, stick to what you want and who you are - and leave the definitions by the wayside. Mono/poly labels are rather meaningless and limiting when looking an individual's particular needs and wants. Likely as not, you have a lot of fluidity and can be either or both depending on your exact circumstances and mindset. If you want more connections, it doesn't make you anything except a person who wants more connections.
Your girlfriend probably puts more emphasis on you ranking her as being more important because you may not be the kind of guy who blindly says whatever their partner wants to hear - possibly.