hi*
Here are some words that match your criteria:

- hi
- hi-fi
- hi-tech
- hiatal hernia
- hiatus
- hiatus hernia
- Hiawatha
- hiba arborvitae
- hibachi
- Hibbertia
- Hibbing
- hibernal
- hibernate
- hibernating
- hibernation
- Hibernia
- hibiscus
- Hibiscus cannabinus
- Hibiscus elatus
- Hibiscus esculentus
- Hibiscus farragei
- Hibiscus heterophyllus
- Hibiscus moschatus
- Hibiscus moscheutos
- Hibiscus mutabilis
- Hibiscus rosa-sinensis
- Hibiscus sabdariffa
- Hibiscus syriacus
- Hibiscus tiliaceus
- Hibiscus trionum
- hiccough
- hiccough nut
- hiccup
- hiccup nut
- hick
- hickey
- Hickock
- hickory
- hickory nut
- hickory pine
- hickory tree
- Hidatsa
- hidden
- hidden reserve
- hidden tax
- hiddenite
- hide
- hide and go seek
- hide out
- hide-and-seek
- hideaway
- hidebound
- Hideki Yukawa
- hideous
- hideously
- hideousness
- hideout
- Hideyo Noguchi
- hiding
- hiding place
- hidrosis
- hidrotic
- hie
- hiemal
- Hieracium
- Hieracium aurantiacum
- Hieracium pilocella
- Hieracium praealtum
- Hieracium venosum
- hierarch
- hierarchal
- hierarchic
- hierarchical
- hierarchical classification system
- hierarchical data structure
- hierarchical menu
- hierarchical structure
- hierarchically
- hierarchy
- hieratic
- hieratic script
- hieratical
- hieroglyph
- hieroglyphic
- hieroglyphical
- hieroglyphically
- hierolatry
- Hieronymus
- Hieronymus Bosch
- hifalutin
- Higginson
- higgle
- higgledy-piggledy
- high
- high altar
- high and low
- High Anglican Church
- High Anglicanism
- high bar
- high beam