She sounds like the jealous/insecure type - I'd ditch her now unless she's amazing in the sack. If she's upset she should call you, no way should you have to call her every day although is sounds like the pair of you don't really communicate when you are talking - seriously if she's getting wound up about you having time to yourself and imagining all sorts it sounds like she's not the trusting type.
No trust = no relationship.
Yup - you have to be open and trust but not all women are confident, sometime it takes them a little time to understand that (a) you love them loads, (b) you trust them and (c) you're not about to run off.
In reality you do have to look into yourself and say - do I have that vibe/feeling when I see her or she walks into the room..
My ex wasn't that and I can say it becomes a chore rather than a relationship, she may have had 32G norks but that doesn't make up for the lack of a spark between the personalities.. certainally no click..
New gf gets attention all the time from guys which makes her weary. Believe it or not we spoke for 4-6 hours (I think it was 4 she says it was 6) online on a dating site before I got to see a photo.. then we spend weeks chatting before we got to skype... then meet in person etc..
I'm often seen as being coldly logical when going out with someone initially often not worrying about chatting between seeing girlfriends again.. then suddenly it clicks - but that's me I've always been like that even with insta-chemistry girls..
With this gf, she's very family orientated. I can see that she's special (at many levels not just physical) and I'm going to put effort in.. sure she's a little demanding on my time but I don't mind - infact there's not much else in the world that matters to me. (man that's clicked in a big way!)
OP- you sound like me. I see my parents a couple of times a year. I have started making an effort (now I'm older) to see them but before I could go a year or two without seeing them. My mum phones every sunday..
So I don't think you're alone thinking that - but it may be worth asking "are you in a relationship for the sake of being in a relationship?".
Three months is a relatively short time.. perhaps give it another month or two and see if it clicks.. just make the effort (all relationships take effort unfortunately - even really great ones) and see how far it goes..