I am on a jobhunt and my 1st interview with Company B went well. To my surprise, the next day, in my current job, I got promoted. I still want to look for a new company and Company B has contacted me for a 2nd interview. And this interview will be with the Senior Manager (1st interview was with the Asst. Manager). Will it be okay to mention about getting promoted in current company? Can I use this promotion as one of my selling-point?
At a minimum, update your LinkedIn profile to reflect your new job title and role.
I don't know enough about your situation to offer solid advice on discussing your promotion with your prospective employer.
My advice would be to continue on with the interviews, without bringing it up explicitly. I would recommend updating any resumes that you submit to other companies as well as any online profiles (such as LinkedIn) that you have. At this time, you don't need to give the company you are interviewing with any updates or changes, since you're in the middle of the interview process.
If Company B comes back to you with an offer, then you can decide what to do. If the offer is worth it, you can accept and give your notice at your current employer. However, if Company B's offer is insufficient, you can negotiate. One point of negotiation may be not accepting a job title that would be a step backwards or a salary that is less than what you are making now.
Without knowing the details of your situation, I can't say that I wouldn't accept a lower salary or a lower title. If you are in a toxic environment, it may be worth it for your career or your health to accept a lower salary (although do make sure you aren't putting yourself in a financially dangerous position). Titles also vary by company - I went from a Senior Software Engineer to a Software Engineer position because I went from a company with 6 different titles to one with 2 - so you may be able to accept or justify a title change.
When it comes time to accept, reject, or negotiate the offer, do so on the merits of the position and what it offers you. Don't get too hung up on the current salary (as long as it is sufficient to meet your needs) or title if it is something that is better for you (especially in the long term).
When a company is about to make a job offer to a new employee they have a concern about a counter offer. They try to determine why the person is looking for a new job, and if they are likely to reject the offer when their current company makes the counter offer.
While it is good that you are continuing to look after receiving the promotion, there is still no guarantee that you will take an offer from the new company. In fact the promotion may have lowered the delta between the old company and the new company.
Telling them about the promotion is likely to make them worried. They now know that you have received a counter offer. They may be worried that the promotion may make it harder to leave. They will be concerned that their second choice will take another job, while you wait the maximum number of days before rejecting them.
Telling them won't be a selling point because they may believe that the promotion is only because the current company was worried you are about to leave. It doesn't tell them about the qualities you have, only that your current company wants to keep you around a little longer because it is an inconvenient time for you to leave.
The general advice is to reject a counteroffer. The general advice is also to not use the counteroffer as a bargaining chip with the new company, because you might lose both jobs. Telling them about the promotion before an offer is even made increases the risk there will be no offer.