I found a duplex that I would like to make an offer. The seller has an agent but I do not. The seller's agent said they can write the contract and do everything else on my behalf. Do I still need an agent to represent me?

If you have to ask, then probably. 

It will cost you nothing to have an agent that will represent your best interests. The sellers agent wants to write it up for you so that their brokerage can get both sides of the commission. 

Aka get an agent. 

Why wouldn't you get your own agent when it costs you nothing and protects your best interests? And if you don't have or never have had an agent, are you sure you found a diamond in the rough here? Chances are no. If the listing agent writes the offer for you, he or she gets paid the whole commission and their fiduciary duty is to the seller first. The listing has a commission for buyers' agents, bring your own. If you already saw the house, outside of an Open House, with the listing agent, there will be an issue with procuring cause and your agent may have to pay a referral fee.

@Karissa Cardenas I have an agent I’ve worked with for about 20 years. He’s the best. I recommend building strong, long lasting relationships with as many people as you can get on your team as possible.

If I need someone like an inspector or a structural engineer I’d rather know my buyers agent referred me to them because they’re excellent rather than the sellers agent because they don’t find any issues and will just sugar coat problems.

Everyone says it costs nothing… but who is the only person spending money? YOU the buyer. 
Your money pays both agents commission, it pays for everything.

Being commissioned based agents are inherently greedy, literally part of the job that they won’t admit to. 

benefits of using the listing broker- feeding the beast

-listing agent wants both sellers and buyers commission and will fight for your deal over other offers even at a lower price because they make more $$$.

If this is your first deal and you aren’t sure what you are doing or looking at it may be better to find an agent. 
if you are pretty familiar with the process it’s really no different who represents you as long as you can stand your ground and represent yourself if needed. 
I purchased a house using the listing agent as my buyers agent, I made an offer that was lower than another competing offer and also negotiated 4% off the initial offer after inspection because I was prepared to walk away. (But I also knew realistically how much repairs cost and submitted contractor bids in my counter offer; representing myself)