schwindelig
dizzy
Having the feeling that everything is spinning and that you might lose your balance; affected by dizziness.
Nach der Karussellfahrt war mir total schwindelig.
After the carousel ride, I was totally dizzy.

dizzy
Loading your saved state.
dizzy
Having the feeling that everything is spinning and that you might lose your balance; affected by dizziness.
Nach der Karussellfahrt war mir total schwindelig.
After the carousel ride, I was totally dizzy.

To express the feeling of dizziness, German uses a dative construction with 'sein' (to be). The person is in the dative. Say 'Mir ist schwindelig' (I feel dizzy), not 'Ich bin schwindelig'.
Mir wird immer schwindelig, wenn ich schnell aufstehe.
I always get dizzy when I stand up quickly.
The adjective 'schwindelig' (dizzy) is derived directly from the noun 'der Schwindel' (dizziness). If you know the noun, you can easily work out the meaning of the adjective.
Der Schwindel war so stark, dass ich mich hinsetzen musste.
The dizziness was so strong that I had to sit down.
The grammatical structure reveals the meaning. 'Mir ist schwindelig' (I feel dizzy) describes a physical sensation. 'Ein schwindeliges Tempo' (a dizzying speed) describes a quality of something. 'Bist du schwindelig?' is a colloquial question that means 'Are you crazy?'
Nach der langen Fahrt war mir etwas schwindelig.
After the long ride, I was a little dizzy.
The meaning 'verrückt' (crazy) or 'unüberlegt' (rash) is colloquial. It is almost always used in an incredulous or rhetorical question to criticize another person's behavior.
Du willst bei diesem Sturm nach draußen gehen? Bist du eigentlich schwindelig?
You want to go outside in this storm? Are you actually crazy?
crazy
'verrückt' and 'schwindelig' can both mean in colloquial speech that someone is not acting sensibly. However, this use of 'schwindelig' is more specific and often appears in questions or reproaches, for example when you think an idea is completely unreasonable. 'verrückt' is much more general and can be used more neutrally. Also important: 'schwindelig' normally means a physical feeling, when everything is spinning. Only in its figurative, colloquial sense does it come close to 'verrückt'.

Bist du schwindelig, bei Glatteis ohne Jacke und ohne Licht loszufahren?
Are you crazy, setting off on icy roads without a jacket and without lights?
Der Chef findet den Plan verrückt, aber das Team möchte ihn trotzdem versuchen.
The boss thinks the plan is crazy, but the team still wants to try it.