Suffering because of silly mistake - replied one E-mail to one of our employees without taking permission of my manager

Try and find a mutual friend whom will try and reconcile both of you. S/he might be your workmate or just somebody from outside. If that fails, you can ask for transfer to another department.

Dear Ms. Swati,
It was observed mostly if a girl's reporting authority belongs to same gender boss then such kind of problem happens. This does not apply in every case but observed in many.
I would suggest you to find another job as you informed that your boss reports to the Director so I don't think it will solve your issue because the Director will definitely favour to your boss. Secondly, if the Director agrees and suggest your boss to keep calm then it might possible your boss may hurt with this and she would create problem in future specially at the time of appraisals and all.
So don't react much, be cool.
I would suggest to find another job without discussing change for the job with anybody in your organization.

Experts in the field have given their suggestions. I would add one more. Time heals every thing. So apply for leave for a week or fifteen days. Things will be settled. You manager also feels the work pressure without you.
All the best.

Dear Mr. Anurag,
I am also thinking the same way you have suggested, but little confusion is there as its being only 2.5yrs since i am working here and as far as my concern it is not a long time, so will it be a right time to switch! or will it effect my career?
do reply!!
Regards
Swaati

Dear Swati,
Having gone through the entire correspondence (suggestions etc) I feel that you have to take two pronged steps in the situation:
1. Approach the Director, explain the entire sequence of event and also the behaviour of your boss seeking his guidance in right earnest. In the process please also express your apprehension very mildly of your boss coming on you heavily after his intervention ; and
2. Start looking out for another job, even though it is at par or so.
S.K.Johri

Hi,
If you are planning for a move then don't even open the issue with your director. You need to move out without any negative vibes.
Once your director is involved he would accept you to continue with the organization.
However, by your luck if you get an opportunity in another company then it will be difficult to complete your notice period.. and also to convence your manager to approve for the resignation...
2.5 years is more than sufficient to look forward.. i keep browsing for HR positions.. i have come across many requirements in Linkedin, Monster ,Naukri..
Don't put down your papers and then start searching.. Start searching and get the offer letter.. and then quit..
Regards,
Radha yermal

Well, in this situation better to keep yourself calm and behave politely and focus on your work more so there should be no any mistake as in this situation even a small mistake by you will make situation worst for you. So keep calm and focus your work behave politely to all including your manager like nothing happened ...and as the time passes everything will be fine.

Madam,
It appear from your write up that their is some problem of Interpersonal relations
and communication gap between you two but I suggest you sit with your Manager
talk one to one.Definitely your manager will come out with the problem and to be
resolved.You will find your Manager will be more caring & will pass on the responsibilities
once you win his ir her trust
Swatantar

It is said that employees 'do not leave the organisation, but the Managers' fits here welll. As a senior person, she should counsel you and ensure you do not repeat such mistakes in future. As my fellow professionals have pointed, try your best to maintain cordial relations with her, keep a low profile for a few more weeks and watch for any improvement in her attitude towards you. In the meanwhile, look for a better job. Before accepting the new job, you can go to your senior management ie. next superior (boss' boss) and explain the sequences of events. Tell him/her that you have no choice but to leave the organisation. Wait for a reaction or response and accordingly take a call whether to continue or quit the job..
Best wishes

Dear Swaati,
Some managers are like this type who are egoistic and do not understand basic fundas. You have only two choices left with you, i.e. is take the matter to your director and tell him what is happening and ask him to mediate and help you or look for a change continuing in the same organisation.
Rameshbala