Everyone bothers everyone at one time or another. Being an empath just means you're more attuned to picking it up when someone is bothered.
I'm not sure how sensitive you are and how clearly you are able to distinguish the energy you're picking up so if I say something that is off or doesn't apply to your experience, I apologize.
Sometimes people will direct a negative feeling at someone else that has nothing to do with it (like maybe they are just having a bad day and any hiccups are triggering more irritation for them). So there could be a chance that what you are picking up might not actually be about you, you're just receiving it. Try not to internalize everything that is sent your way, the more you take in the more you are going to feel crappy in general. There's some people out there that are plain toxic, so no matter what, if you spend time near/with them you are going to be negatively impacted. When we take on (or are exposed to) the negative energy of others our own energy can be distorted. So your feelings of not being liked could also be coming from the fact that your energy has been 'tainted' and not that its actually that you are disliked. Another fun thing empaths get to experience is at times, you can take on someone else's feelings It probably more typically happens with people that you are close to (emotionally)but if you are very sensitive you could get it from strange also. If that's the case, I'd advice trying to make sure that the feeling you are having is yours and not something you may have picked up from someone else.
Honestly as an empath, other people are probably going to bother you a lot more than you would them. Trying to create an emotional/energy barrier (boundaries) for yourself I think will help so you won't take on too much from others. Another thing that is important is allowing yourself time to 'clear'. Time to yourself, to relax, to do something enjoyable, or to try to transfer the negative feelings to something else.
_________________
"Inside the heart of each and every one of us there is a longing to be understood by someone who really cares. When a person is understood, he or she can put up with almost anything in the world."