If all sites on that host are down, then it only confirms my guess that your site was hacked on a server level. Sounds like a host who has no (good) control over their security.
Try another host? I would not be very confident to stay with the same host after such thing happened, but also depending on how they react to a situation like this, how long it will take them to get things sorted, if they can give some degree of garantee that vulnerabilities have been closed, etc...
I can not suggest any specific host, but there is no such thing as "unlimited", for me a claim like that put up red flags.
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