32-Year-Old Manager Seeking Help to Improve Image with Team and Peers

Ans: Hi!!
You are just 32 and you are handling a team of 15, that's a good space to be in. Congratulations!!
Let me dissect your message and answer each requirement one by one..
1. "I need some help in rebuilding the positive image in front of my team and peers and even seniors" -
The first step to change is recognising that a change is needed. For you to improve your image in front of your team, peers and seniors you need to work on your communication skills, your negotiation skills and your leadership skills.
2."i have got this feedback that my tone is pushy/ Rude.. even though that's not the case from my perspective"
You make not be pushy and rude in your heart, but if the feedback is this from the majority of people then you need to look into it...that's why I always say, "it's not what you say but how you say it", try adding warmth in your tone when you speak, smile, see if you can make others comfortable in your presence. Check you body language, is it open and inviting?
3 " I need to make my image as approachable manager with Good skills and good behavior and attitude." - there is work to be done here. This can be achieved in terms of making a change in your clothing ( the cut of your clothes, the choice of colours, fabric, the prints, it's a whole science of clothing at work), your verbal and non verbal communication and finally working on your mindset.
See if we can connect one on one. All your targets are achievable and learnable skills!!

All the best to you!!