The reality star gave birth on Mother's Day (Sunday 6 March), and this weekend she shared a touching black and white photo of her son's hands.
She said via Twitter: "Sunday cuddles with my little man could not be any more perfect."
Alex welcomed her first child with ex-boyfriend Charles Martin. They are yet to reveal the name of their son.
After welcoming her boy, Alex said: "Nobody can prepare you for this feeling, most amazing Mother's Day ever."
Announcing her baby news last November, Alex admitted she hadn't meant to fall pregnant, but revealed her excitement at becoming a mum.
She revealed at the time: "I am delighted to announce that my secret is out and me and Charles are expecting a baby boy! Although it was a huge shock, and we have been through some really tough times, we are now really excited to meet our little one."
Alex and Charles initially split last summer after she came clean about cheating on him. However, they managed to patch up their differences and give their relationship another go, but recently split again.
Alex said in her new! magazine column this month (2 March): "Charles and I are in a good place at the moment. I've seen him quite a bit this week. We've got to a nice stage where we do talk, but we're just friends, there's nothing more to it. We get along really well - it's only taken nine months, but we're finally there!"
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