If you do not want a child, then you absolutely should not have one. A child should never be put into a family where one parent resents it, and doesn't give it the love and time it deserves, or who gives it begrudgingly. Children sense when they are wanted.
There is nothing wrong with you not wanting to have a child, but you must realize that there is also nothing wrong with your wife wanting to have a child. What you must decide for yourselves is whether or not this is a make it or break it situation for the two of you. If she is wanting a child now, at 28, this feeling will only intensify, the older she gets. She may then begin to deeply resent you because you have kept her from having a child, which would ruin the marriage you want to keep in tact to begin with.
These are things that should have been worked out before you married, but feelings change, opinions change, and people change, grow, become different as time goes on. A christian counselor and/or pastoral counselor is going to be able to help you both in some aspects but what it will boil down to is this: Am I willing to give up my marriage to stick with my decision to have or not to have children?
That's a question you'll both have to ask yourselves, and unfortunately, it may mean the end of your relationship if you can't come to an agreement without forcing one to compromise.
My advice for you both, not just you, is this:
Pray.
Ask God to help you to make the right choice.
Ask him if there is something in you that needs work, or changing, and if there is, tell him that you want him to help you change.
Finally, trust God to know what is best for you, and if you can't do that, then the issue here isn't having children, it's your faith.
By the way, you shouldn't feel ashamed for having these worries or feelings. It's good that you are in touch with how you feel. Sometimes men can't pinpoint why they feel as they do, but you seem to have a good handle on what it is about having a child that concerns you. Know this one thing though; you'll age, and your feelings may change. Some day you may feel ready for children, but that may come at a time when your wife is no longer physically capable to do so, and this could become a time when she would resent you the most. Something to keep in mind.
I'll pray for you both too.