According to utilitarianism as "the greatest good for the greatest number," absolutely, you should take actions that maximize the well-being of all.
The terminology is mildly confusing here because we often use "utilitarianism" to refer to any sort of consistent consequentialism, and consequentialism can be selfish. But classic utilitarianism is very much altruistic.
Rational utilitarianism means maximizing your own expected utility. (Technically from the gene's perspective; so caring for your children is selfish.) Social contracts (voting, laws against killing, etc) are just the game theoretical result of everyone acting selfishly.
It's about selfishness not altruism.
Utilitarianism seems to indicate that the greatest good for the most people generally revolves around their feelings. A person feeling happy and confident is a desired state, a person in pain and misery is undesirable.
But what about taking selfish actions that hurt another person's feelings? If I'm in a relationship and breaking up with her would hurt her feelings, does that mean I have a moral obligation to stay with her? If I have an employee who is well-meaning but isn't working out, am I morally allowed to fire him? Or what about at a club? A guy is talking to a woman, and she's ready to go home with him. I could socially tool him and take her home myself, but doing so would cause him greater unhappiness than I would have felt if I'd left them alone.
In a nutshell, does utilitarianism state that I am morally obliged to curb my selfish desires so that other people can be happy?