I would go for a new host.
Based on the responses you post here, I am with Matt on this that your host is probably overselling or have a poorly configured resource limiter. I suggest you go to a reputable community to get more information about your current host and to search for a new one if you decide to. While this community is still not on the right software, it is the largest one out there: https://www.webhostingtalk.com/
If you have a huge site and need a VPN or dedicated solution, toss me a message and I can send you a contact I used when I was hosting. He has good prices and good reputation.