It's so soon into your relationship. Of course you are finding this a bit strange, because it IS strange to you.
Why do you only see him once or twice a week? Is this your decision, his or life gets in the way.
Honey, I am so saddened that someone as young as you has suffered so much, pretty much ALL of your relationship-life. How on earth could you know any different?
Can I ask you just to take it a day at a time, think about what this new guy is offering you, and enjoy the good times, get used to them. Enjoy being valued, respected, loved, desired and wanted. Be your best friend, be kind to yourself and to him and see where it goes.
As I said, this relationship is new, not only in length for you both, but new to you as a concept. Take it steady, learn how you ought to be treated and enjoy it.
If you are looking for excitement on the days you don't see him, see if you can find something you enjoy for YOU, a class, a gym, a hobby, something to give you back your life, your fun and enjoyment. Stuff you ought to be enjoying at the ripe old age of 24.
You will get through this, you might find in time you may be able to reduce or even remove the ADs from your life.
I wish you all the luck in the world, sounds like you deserve it!