Is Lord Nityananda the incarnation of Sri Balarama?
According to Chaitanya Charitamrta and Gaudiya Vaishnava view, yes he is:
sei kṛṣṇa navadvīpe śrī-caitanya-candra
sei balarāma saṅge śrī-nityānanda [CC - 1.5.6]
That original Lord Kṛṣṇa appeared in Navadvīpa as Lord Caitanya, and Balarāma appeared with Him as Lord Nityānanda.
sarva-rūpe āsvādaye kṛṣṇa-sevānanda
sei balarāma — gaura-saṅge nityānanda [CC - 1.5.11]
In all the forms He tastes the transcendental bliss of serving Kṛṣṇa. That same Balarāma is Lord Nityānanda, the companion of Lord Gaurasundara.
The 5th chapter of Adi Lila in Chaitanya Charitamrita describes in detail about Lord Nityananda Balarama.
In addition to the above answer, there are also a few scriptural injunctions that the Goswamis quote to support that Lord Nityananda is Balaram Himself
Vayu Purana states:
balaramo mamaivamsah, so 'pi mat-prstham esyati; nityananda iti khyato nyasi-cudamanih ksitau
"In the Vayu Purana, the Lord tells Brahma: "Lord Balarama, who is My first expansion and non-different from Me will also appear by My side as Lord Shri Nityananda. He will become the crest jewel of all renunciants on the earth.""
krtvavadhuta-vesam sa, dharman bhagavatan bahun; grahayitva janan ittham grhinam asramam tatah.
"Assuming the dress of an avadhuta, He will freely distribute bhagavata dharma i.e. love of God. He will distribute this pure love through various means and deliver all the living entities. He will do so first as a brahmacari and later as a householder."
Ananta Samhita states:
nityanando maha-kayo, bhutva mat-kirtane ratah; vimudhan bhakti-rahitan, mama bhaktan karisyasi.
"When I appear in Navadvipa in Kali-yuga, You will become Nityananda. You will have a very tall, beautiful and large body, and You will be constantly absorbed in chanting My name and glories. In this way, by Your causeless mercy You will convert many bewildered fools who are devoid of devotion into My pure unalloyed devotees."
Note however, this verses are generally not accepted by any school other then Gaudiyas. If you believe that Lord Nityanada is Balaram Himself, then you are in essence a Gaudiya also. Jaya Nitai!