You may be over thinking it, but you also have reason to worry. You are at an age in which peers and social relationships are very important, so I can see how not feeling like you have friends could be very concerning to you. However, from your mother’s perspective it may not seem like that big of a deal — certainly not bad enough to seek professional help. It also sounds like you aren’t as depressed as you were right after the move, which is good, but I’m wondering if you spoke to your mom about your feelings then. If she understands how hard all the changes have been for you she might be more supportive… and it’s not too late to do that.
If you don’t get anywhere with your mom, I would suggest that you speak to your school counselor or nurse, as well as looking into resources on your own. I’m not familiar with the services in your country, but in the US adolescents can initiate therapy on their own for at least a few sessions. You might also be able to find a free support group in your community that might be helpful.
Otherwise, you are doing the right things by trying hard to make friends. The more situations you are in, the more likely it is that you will connect to someone. So I would recommend joining clubs or sports, look for volunteer opportunities, etc. Keep trying and it will pay off in the end. Whatever you do, just don’t give up.