How long have you been together? If your relationship is new then she needs to build up the trust a bit if she's a bit of an insecure person or has been hurt in the past. Sometimes it's a trait of the insecure or anxious to look for things that are going wrong when everything is perfectly fine, I am guilty of this myself sometimes.
The only thing you can do, and I highly recommend it, is that you reassure, reassure, reassure. If she has insecurity then the only thing you can do is be supportive and let her know that you will not be unfaithful and that you love her. Likes on Facebook are only as meaningful as you make them, and it would be good for her to hear this from you. When you like your girlfriend's picture it probably means "you are beautiful", when you liked that picture, as you say, it just meant you were happy for her in her new relationship. You can't take away the insecurity or fix it for her, she has to do that herself. Just do your part and love her as normal and eventually the message will sink in.
If she starts accusing you of cheating or something though I would suggest you assess the relationship. You need to be able to trust each other and if she actually starts to think you're cheating on her because of Facebook likes then there is a severe lack of trust and a big dose of insecurity which isn't healthy. Small amount of jealousy is somewhat normal and can be handled by both partners if done properly, but if it goes on for too long or goes too far you should probably reconsider the relationship.
If you say this;
"""I only liked it because I was happy she got into a relationship, not because I was attracted to her. The "is in a new relationship with guy" and happy selfie picture were both posted at the same time. Hell all of my other friends liked it too, I thought it was just my way of saying congratulations"""
to your girlfriend then she shouldn't need any more than that. I would be perfectly fine and reassured by this if I needed it.