Does nutrition fall under the branch of biology?

both biology and health

Almost

Aerobiology • Anatomy • Arachnology • Astrobiology

Bacteriology • Batrachology • Biochemistry • Bionics • Biogeography • Bioinformatics • Biological psychiatry • Biomechanics • Biomedical • Biophysics • Biotechnology • Botany

Cell biology • Chorology • Cladistics • Carcinology • Computational biology • Cryptozoology • Cycles • Cytology • Conservation biology

Dendrology • Developmental biology • Disease (Genetic diseases, Infectious diseases)

Ecology (Theoretical ecology, Symbiology, Autecology, Synecology) • Environmental science • Epidemiology • Ethology • Entomology • Evolutionary biology (Evolution) • Evolutionary developmental biology • Endocrinology • Enzymology • Embryology • Exobiology

Freshwater biology

Genetics (Population genetics, Quantitative genetics, Genomics, Proteomics)

Herpetology • Histology • Human biology

Ichthyology • Immunology • Infectious diseases

Limnology

Malacology • Mammalogy • Marine biology • Matrix biology • Medicine • Microbiology (Bacteriology) • Molecular biology • Morphology • Mycology (Lichenology) • Myrmecology • Microbiology

Nematology • Neuroscience (Neuroanatomy, Neurophysiology, Systems neuroscience, Biological psychology, Psychiatry, Psychopharmacology, Behavioral science, Neuroethology, Psychophysics, Computational neuroscience, Cognitive neuroscience, Cognitive science)

Oncology • Ontogeny • Ophiology • Origin of life • Ornithology

Paleontology (Paleobotany, Paleozoology) • Parasitology • Pathology • Pharmacology • Photobiology • Phycology (Algology) • Phylogeny (Phylogenetics, Phylogeography) • Physiology • Phytopathology • Population biology • Protistology

Quantum biology

Reproductive biology

Scatology • Structural biology • Systems biology • Synthetic biology • Sociobiology • Symbiology

Taxonomy • Toxicology

Virology • Veterinary medicine

Xenobiology

Zoology

But not quite. It might be under Human Biology if anything

It's its own category.

A general rule of thumb - if an undergraduate course can be taught on it, it is usually its own subject.

Psychology is the best choice.