Hi Felgonre, sorry to hear you're having traffic trouble. When I see a situation like this, it usually comes down to one of a few factors. I hope that by providing some resources, you will be able to determine what the issue is.
1). Dramatic increase in site traffic. This is a good thing! In situations like this, you just have to upgrade so that you have more resources. You can determine if this is the case by carefully analyzing your site's performance in AWStats or with other metrics.
2). You have an increase in site traffic, but it's all bots. This is also something you can learn by analyzing your site statistics. To solve this issue, you will need to edit the robots.txt file and maybe enact other measures. I often recommend people try CloudFlare's free tier, which comes with DDOS protection that also helps with bot traffic.
3). You actually are suffering a DDOS attack. The solution to this is similar to #2.
4). You are suffering from a brute force login attack-- especially common on WordPress sites with default settings. Treat this like a DDOS (i.e. CloudFlare), but also consider using one or more of the many pieces of software built into cPanel or packaged as a plugin to deal with the issue.
5). There is an optimization issue draining your resources. With a WordPress site, this often involves poor Admin Ajax optimization. I once saw a popular website with a 500 MB image on the front page, even though the image was actually quite small. Every visitor was draining server resources to download one poorly optimized image!
Usually the issue is 2, 3, 4, or 5. If you have investigated all of those and found nothing I would consider an upgrade, but usually that is one of the issues. Hope that helps!