How to solve the problem with sites exceed resource usage in shared hosting plans?

[Emilio]

I have a site running on a shared hosting plan and sometimes it exceeded resource of the hosting package allowed.

How to solve this problem? any advice?

 

[Localnode]

Which resources? Space, bandwidth? Or CPU/Memory/inodes, etc. limits?
What is your website based on? Meaning if a CMS - which CMS. Or HTML/PHP static, etc.

 

[Emilio]

Which resources? Space, bandwidth? Or CPU/Memory/inodes, etc. limits?

CPU and memory. I got warrnings about mysql queries

What is your website based on? Meaning if a CMS - which CMS. Or HTML/PHP static, etc.

Wordpress sites. I was recommended to update to a new hosting/VPS. Is it a good move?

 

[Localnode]

Localnode

As RDO Servers said, optimise your website.
cPanel instructions like so:
http://i.imgur.com/sZT8smc.png
http://i.imgur.com/N15Lv2b.png

Search for "Optimize Website" in cPanel, then follow the images. When done, hit "Update Settings".
Look at getting a CDN like CloudFlare - free option is great, they have their own Wordpress plugin.

WP Super Cache is a great plugin, and will help with the load. Other options are "Cache Enabler" which has fewer customisation options, and is easier.

WP Super Cache plugin installation/setup guides are all over the Internet. A quick Google will return many results.

This should help dramatically. If you're still using too much resources, then you may need to upgrade. But in most cases, these things tend to be the result of a poorly optimised WP install.
How big is your website and database?

 

[vishwa]

If you have high amount of plugins installed in your WordPress site than you might have to remove unnecessary plugins. Bad plugins can use enormous amount of resources of your server. However if you still need those plugins than you have to opted for VPS hosting plans.

 

[RDO Servers]

Always start with optimising your website.

Go through your site and remove any unnecessary plugins.
Next, run a test on GTMetrix or Pingdom speed test and see what it recommends.
Then you can consider upgrading your hosting if you are still running out of resources.

WordPress sites are the worst for resource consumption. Plugins are great, but that all cause a decrease in performance. (More code to run = more work the server has to do)