It's absolutely normal for sensitive people to feel emotions from people around them. There are ways though that you avoid suffering.
Normally a sensitive person doesn't suffer with empathy, it's an absolutely normal thing and it can be used also as a tool. But if as a child they were trying to force you to feel certain things or avoiding others, you know, "stop being too sensitive", then you start judging the feelings, either they are yours or not.
Even in these case you can find ways to stop suffering.
1. Don't take over these emotions. They are not yours. Always try to remind it to yourself. You are not guilty if someone feels bad, just see it as an information.
2. Let these feeling pass through you and go away. If you try to protect yourself you make a nest and hold on to them. If you let your body and mind be open you will see them going away as they came.
3. Try to recognize and separate these emotions, recognize positive from negative, normal from crazy etc.
4. Play with them. Make stories by observing the surrounding people together with feeling these emotions. It's like when you are in a car, you get less dizzy when you look outside.
Find out who is admiring whom, or even being in love, who hates whom, who finds whom interesting. Also who admires you ;-)
The whole thing is to understand that feelings, just like thoughts, yours or everybody's, are automatic processes, maybe people think that they control them but this is not true. If you realize this you will not take them as seriously as you do now.
Maybe feeling other people can be a tool to help them, but don't try it if you feel resistance from them. You know, many people feel just like you, everyone's feeling.