I heard that Laxman is an avatar of Sheshnag? Is this true?
Yes, Shree Laxman and Balraam both are the avatars of Sheshnag. In Padma Puran there is a Chapter 1.5.11, The proof is mentioned here in this chapter. According this: When lord Mahadev was telling the story of Sri Ram to Parvati here he mentioned about Sri Laxman.
Lord Mahadeva told Parvati- "Dasharath requested Vashishth to perform the Jaatkarm Sanskar of Sri Ram. In course of time Kaikeyi gave birth to Bharat- an incarnation of Panchajanya conch. Similarly,
Sumitra gave birth to two sons--Laxman and Shatrughan. Laxman was the incarnation of Sheshnag while Shatrughan was the incarnation of Sudershan chakra.
Sri Ram and his brothers received education under the guidance of Sage Vashishth.
In a very short time they became proficient in all the scriptures and mastered various weaponaries. Although all the four brothers were very close to each other, yet Laxman could not bear to live in Ram's separation even for a moment and was specially close to him."
Link: Padma Purana
Another Proof, When Goswami Tulsidas was praying to Sri Laxman he also describes him as a Avatar of Sheshnag in below lines...
बंर्दौं लछिमन पद जलजाता। सीतल सुभग भगत सुखदात।।
रघुपति कीरति बिमल पताका। द्वंड समान भयउ जस जाका।।
सेष सहस्रसीस जगकारन। जो अवतरेउ भूमि भय टारन।।
Yes,this is true.
In the Treta Yuga, Lord Vishnu took seventh avatar as Lord Rama. Sheshnag accompanied him and took avatar as Lakshman–the younger brother.
Refer this good article.