Hello Nicky, welcome to the forum.
The scenario of not appreciating, or even wanting, what you have until it'a gone, is quite a well-known one ~ as is the one where one where one party is more interested than the other ~ until that party loses intererst.
If you didn't feel much for her, and didn't particularly want to be with her ('I never really missed her'), why did you start the relationship in the first place? Was this just a physical thing ('maybe it was just lust')? Perhaps you are confusing affection with desire.
If she is still only 19 and has been in relationships since the age of 16, I can understand her needing time to sort herself out. Sixteen is very young ~ too young I think ~ to be involved in a serious long-term relationship.
She may well really like you, and, at 19, may even be ready for a proper relationship, but she probably needs to sort out her life and her feelings first.
Sixteen is little more than a child, yet she was in a committed relationship for two years from that age ~ with someone who cheated on her. Yes, I think she may need some time for herself before embarking on another commitment.
You have also needed time on your own after a long relationship, so you may understand. ('i love being single')
I can really understand why you think that you should either be together or not be together. However, I can see her need for a break ~ not just from you, but from relationships.
Maybe you are confused because all you thought that you wanted was to be single and to satisfy your lust, but you discovered someone you cared about ~ but who isn't ready for you.
You need to think about what you want & feel and what she wants & feels.
If she feels affection for you and you only feel lust, then that will not be fair on her.
If you both need to be single after a long-term relationship, then that may make sense, but you both need to respect each other's needs.
If you really think that you care about her, then give her time and let the relationship have a chance.
Whatever you choose to do, be honest ~ with her and with yourself.
To be uninterested in her, while she cares for you, isn't fair.
To be in lust with someone, who feels true affection, isn't fair.
To know that you need to be single, without acknowledging that she has that same need, isn't fair.
If you both feel the same way ~ and it seems that you do, in many ways, then why not have a serious honest discussion with her and give yourselves a chance. Maybe it won't work out or may be it will.
Why not 'wait around for a few weeks' until you have a clear answer?
You are young and single and you had chosen not to have a girlfriend in three years, so a few weeks shouldn't be a major problem. You had only been dating for a few weeks, during which time neither of you seem to have known, for sure, how you felt or what you wanted.
Give yourselves a break and a chance.