Based on the limited information that you have provided, you (and/or your network administrator) do not yet have the skills necessary to manage your own web server. Therefore, your best course of action is to switch to an outside web hosting provider.
This is no cause for shame: most small and medium-sized companies use outside providers for web hosting even if they do have the requisite in-house expertise. Companies do this because outside providers that specialize in web hosting can provide better performance, uptime, and security monitoring than one would expect from a typical in-house web server.
Be sure that whatever plan or package you choose is:
- Fully managed
- Scaled appropriately for the amount of traffic that your site receives
- Not an "unlimited" plan (all hosting plans have usage limits, but some hosting companies lie)
You will need to be extremely careful about how you manage the DNS cutover from the old site to the new site. Some web hosting companies (e.g. Liquid Web) will help you to perform a clean migration from your existing site at no additional cost.