Adjective for a decision that had no real alternative

You may use inevitable:

• Impossible to avoid or prevent; certain to happen.

(AHD)

Your choice was a foregone conclusion, also sometimes expressed as fore-drawn conclusion.

adj., ineluctable

• impossible to avoid or evade
• My decision to attend university X was ineluctable..

A five syllable beauty like ineluctable is obviously not the kind of word you throw around in daily speech. It's far more often used as a written word, as in the common phrase "ineluctable conclusion." (vocab.com)

It is a Hobson's choice (in comments..)

Hobson had an extensive stable of some 40 horses. This gave the appearance to his customers that, upon entry, that customer would have his or her choice of mounts, when in fact there was only one:

• Where to elect there is but one, / 'Tis Hobson's choice—take that, or none.

(wiki)

Obligatory is the synonym I'd choose here.

obligatory adjective

1 forcing one's compliance or participation by or as if by law ...

Synonyms compulsory, forced, imperative, incumbent, involuntary, necessary, nonelective, obligatory, peremptory, required

[Merriam-Webster]