I can't skate with my new skates; any advise or experience you might like to share?

I've been ice skating for about three months. I've been taking group lessons for about a month too. I was no ice dancing champion, but I was very confident going forward, I could do a snow-plough stop, and I had just started going backwards. I had always used rental hockey skates up until this week when I decided to invest in a pair of my very own hockey skates. They are the Nike-Bauer Ignite 22 skates. When I got them on, to my horror, I couldn't skate in them. They felt all wrong. I haven't fallen for a couple of months; but last night I fell twice in one hour. The blades seem to catch and drag on the ice. The blades don't feel like they want to go through the ice, but they are sharp: I got them sharpened right after I bought them. If I lean too far forwards then the blade digs in and if I don't lean back I fall forwards. These are hockey skates and don't have toe-picks! Even when I'm gliding there's a lot of friction between the blade and the ice. This makes an uneven glide and one foot starts to overtake the other. It's a total nightmare. I hated every second on the ice, and feel really disappointed and disheartened. I ran my finger along the side of the edges and they feel rough. Like there are little spiky bits that haven't been ground off properly. I'm wondering if this is the problem. They are carbon blades too. Would the rental skates have been steel? Maybe the blades are made from a different material? Is it normal to struggle with new skates? Any advise, or experience that you might like to share?