Hi Signum,
I've always been sensitive to other people's feelings. I expect it is easier if you are female as people aren't so surprised by it. I'm guessing it is harder if you are a young guy because it goes against the norm. That's not to say guys can't intuit feelings it's just that there is a lot of societal pressure not to show it and shove all those feeling down under macho bravado.
So where do you start and what do you do with it? Well the first thing to realise is that you have a talent for this. A gift if you like. However talent without discipline doesn't get very far. You need to learn how to control and develop it.
What you need to do first is learn how to ground yourself and not pick up emotions when you don't want to. It is very draining to absorb everything from everyone so learning how to switch it off and on at will will protect you and enable you to socialise when you choose. This was a very important part of my training. When I first started learning to do energy healing as soon as I touched a practise client I would absorb all their pain and burst into tears! Not very helpful for the client and not fun for me either. I had to learn how to deal with the painful emotions inside me so I could switch them off and help others. (I did this through EFT and other energy healing. I also think being Reiki attuned helped me learn how to channel energy and ground myself). It wasn't an instant process, but a persistant work on dealing with those uncomfortable feelings.
The next thing you need to do is learn how to develop your strength even further so you can use it to help others. I really enjoyened Sonia Choquette's book "Diary of a Psychic" in that it showed her development of her psychic skills. Yes she had a natural talent in communicating with the spirit world, but she had to learn how to trust and use it. It also showed that using your gifts isn't always the easiest path, but it is the most interesting! Now your skill is different as it is empathy rather than psychic, but I think you would find a lot a parallels in how to develop it. It would be great if you could find a mentor to teach you. You might want to consider putting out a request via LOA that the right mentor comes into your life to assist you with your development.
It can be very painful being privy to the feelings of others, it is also a priviledge and one that you can use to help them. I'm sure with the right development you will find the path that enables you to use it well.