Firstly - congratulations!
Secondly - slow down!
So, this is your first ever relationship? Have you heard of NRE? You can Google it, or search on here, through the forum. It means New Relationship Energy. It's that buzz that most people feel (whether monogamous or poly) when they meet someone they click with. It can last anything from around 2 months to even a year or two. I've found that, for me, it lasts about 3 months with those I haven't fallen in love with and about 6 months with those I am in love with.
It's that can't stop thinking about them, would change my life for them, would spend the rest of my days with them, want to talk to them every minute and see them every day warm fuzziness. It's that can't wait to tear each other's clothes off new lust.
There are a couple of important things to bear in mind:
1. Most importantly - have you guys sat down and defined roles? Are you their sex partner, their secondary, a potential joint primary? Are they open to love and emotion, or do they just want something physical? How do they want things to go now and what would they consider in the future?
How does this look in reality? Asking things like "what am I to you? what are the boundaries and guidelines?" Outlining how often you're planning to see each other. Once a week? Twice a week? More?
2. Don't push. Nothing kills something beautiful like pushing.
How does this look in reality? Agreeing on a schedule and sticking to it. Them not breaking promises or cancelling without good reason. You not pouting or persuading if they are meeting the agreement, but you want more. Don't accept "we'll see you whenever we feel like it; let's keep it spontaneous" if you're not happy with it.
I have a technique I use when I am falling for someone and don't want to overwhelm them. I call this The 2:1 technique:
Whoever has made the first move two times in a row steps back and lets the other party make the third.
For example, I send the first good morning texts two times in a row? I wait for them to send the next one. I suggest going on an actual date, two times in a row? I let them suggest the next one.
In an ideal world, everything would be equal. But it rarely is. This works brilliantly for me, because it stops me getting carried away - and it also stops me playing games or appearing too aloof. I dated a girl last year who was always the first to text, always suggested the dates, always wanted to talk more and never really gave me a chance to chase. I hate to say this, but her eager availability initially made me see her as part of the furniture, took away the excitement.. and after a few months, became very very claustrophobic for me.
So, if you find some sort of way of holding yourself back, whilst still showing an interest, you should find some sort of balance and ensure that you aren't being to pushy, or being taken for granted.
3. Don't expect to be thought of as each of them are. i.e. you won't be at wife or husband's level right away, if ever. My girlfriend has a husband and when we met, she wasn't looking for a second primary. After about 6 weeks, we fell in love. After 6 months, we started dating regularly. After a year, she called me a joint primary. After two years she says she feels equal love and commitment, wants to give equal time and attention, to each of us. Summary: one month in, I was outside of their marriage - two years in, I am a part of their marriage. We have constantly talked about our roles and I did not assume that I was anything like a girlfriend to my partner, until she actually started using the word. When she did, we discussed it and agreed on it. It's important to know where you stand.
I hope some of this helps!