Well, I can't do your homework for you of course, but first, here are the formats for all three kinds of poetry:
* Sonnet (English or Shakespearean) is comprised of 14 lines, each line containing ten syllables and written in iambic pentameter. There is a pattern of an unemphasized syllable followed by an emphasized syllable repeated five times. The rhyme scheme in a Shakespearean/English sonnet is a-b-a-b, c-d-c-d, e-f-e-f, g-g; the last two lines are a rhyming couplet.
* Sestina is a very structured poem consisting of 6 six-line stanzas followed by a tercet, which is called its envoy or tornada, totaling of thirty-nine lines. The same set of six words ends the lines of each of the six-line stanzas, but in a different order each time. English sestinas are traditionally written in iambic pentameter or another decasyllabic meter.
* Villanelle can only have two rhyme sounds. The first and third lines of the first stanza are rhyming refrains. These refrains alternate as the third line in each successive stanza and form a couplet at the close. This poem form is nineteen lines long, consisting of five tercets and one concluding quatrain.
Points you may want to consider about Hamlet and Ophelia's insanity for your poems:
* It's one of the great debates if Hamlet is actually insane or pretending all the way through the play. It can definitely be argued that he starts by pretending he's insane and then becomes insane in actuality.
* Ophelia definitely, however has her mind snapped starting with Hamlet's poor treatment of her and fully snapping when her father is murdered. Whether or not she intentionally kills herself or not is also a matter of great debate.
* For poetic purposes, you may want to consider using Ophelia's drowning and Hamlet's discovery of her death (and his sickening realization that he drove the woman that he once loved to it) as your starting point.
I'm enclosing a modern student interpretation on Ophelia's death from Youtube to further inspire you!