You basically have two options:
- a) Simply play by the accepted social rules, bring along some cake, stand next to it, do some small talk and accept any congratulations you may get.
- b) Do what you feel is right, and don't bring anything, or only to people you like.
Option a) will avoid the complaints from coworkers, and show you are making an effort to fit in. However, it may feel "fake" to you, or as you write, you may feel "incapable of putting a good face to people that are not nice to me".
Option b) may well exacerbate tensions with your co-workers (or it may not make a difference).
Both options are acceptable in principle, neither is illegal, so it is up to you to decide what you value most.
Finally, I think you will have to tackle the underlying problem, namely that you do not get along with many of your coworkers. While you can work like this for a while, you will get all kinds of problems in the long run: Your work will be unecessarily stressful, cooperation / teamwork will be difficult, you may be perceived as "not a teamplayer". So I think you will have to solve that problem.
How to do that is again up to you (make amends with coworkers, move to different department, quit job...), but you should not let the problem linger. You might consider professional counseling (away from the office) to help you tackle this.