Client has changed the usage patterns (pre-holiday effects before the long Christmas holidays) of the software developed and supplied by the company for which I am working and new errors due to parallel access has surfaced. I am trying my best to correct the situation but still I have not enough time and I have to inform that issues will be solved later. I have some suffering, how to avoid it, what to do?
This is a typical occurrence in software development: it's impossible to anticipate every use case, or guard against every possible way your client may break the application you've worked on.
Even if you think you've done so, it's a certainty that some client, at some point, will break your app in a way that you can't possibly have imagined.
As to how to handle it, here is my perspective (note: my background is technology within a North America finance context):
TL;DR - Focus on resolving the issue. Try to separate professional issues from your personal mental state.
Realize this is NOT personal
Your usage of the phrase "mental suffering" implies that you are taking a professional issue (a software problem) personally. Software issues are not personal character flaws, and do not reflect on your self-worth. Your manager (if you have one) should be enforcing this divide clearly: mistakes happen. Beating yourself up over it isn't the answer.
From a purely pragmatic standpoint: you experiencing "mental suffering" because of a technical issue, doesn't actually help resolve the problem. If anything, you being stressed out will make it more difficult to help the client with the issues.
So, before anything else, please try to re-frame this issue as what it is: a technical issue at work, which is a very common occurrence, and isn't worthy of impacting your personal mental state.
Now that you've done that....(or tried to...)
Make sure the client (and stakeholders on your end) knows you have ownership of the issue
Communication goes a long way: if you haven't already, make sure the customer understands that you understand, acknowledge, and are owning the issue. Ownership is what matters here. Ownership. And communication.
One email can mean the difference between a reasonable client, and an irate one.
At the same time, make sure anyone on your end who needs to know about the issue, knows. Having your boss chase you because they had no idea large client X was having an outage, will not help your stress level.
Identity what you need to fix the problem (time and resources)
Is there something you can do as a workaround to placate the customer? More instances of the application? Different load balancing? If you can do anything as a quick band-aid fix, do it.
Then, focus on the actual problem:
Do you know what has to be done? Do you have everything you need to do that? Do you know how long it will take to fix?
If the answer to any of those questions is no: figure them out. If you need help, find it. If you need to do RCA, do it.
Go back to the people who you communicated with previously. Explain your ownership. Explain your timeline. Explain how you're going to mitigate the issue.
Focus on the resolution: nobody, and I mean this truthfully: nobody cares if you feel bad about this. What they want to know is: how are you going to fix it?
Make good on your word
Fix the problem, understand how to avoid it re-occurring, and take a deep breath.
You did your job. You did well.
This mistake does not define you.
Go do something you enjoy, reward yourself.
Then go back to work, find the co-worker going through the same thing, and help them through it.