If you start the sentence with "I have to.".. then you should use the same verb at the end, e.g. " haven't I?"

If you start the same sentence with "I must " .. then you should also match the verb later with "mustn't I?"

You could use either of these verbs in the context you have quoted, so long as you use the same verb in the sentence.

For example: "

"I have to do the washing-up before I can get my pocket money, haven't I?"

"I must put the cat out before I go to bed, mustn't I?"

"I did brush my teeth, didn't I?"

Hope that helps!

Here's a useful tip:

If you want to know how to form a question tag, just look at the same construction in the question and negative forms.

If you do that, you'll realise that 'I have to finish my homework........ , don't I?' is the only possible tag in standard modern English.

Just look at the use of the auxiliary 'do' in these sentences.

'Do I have to finish my homework?'

'I don't have to finish my homework.'

We don't say 'Have I to finish my homework?'  or 'I haven't to finish my homework' in modern English, so we can't use the 'have I?' tag here.

The only time we use 'have..?' in a tag question is when 'have' is an auxiliary verb in the present perfect tense. For example, 'You haven't locked the door, have you?'.

While 'I have to........haven't I?' or 'I must.....mustn't I?' are grammatically logical, we don't generally use them any more. They sound like something out of a formal textbook written a hundred years ago.

"Haven't I" is possible in colloquial English, I guess, but I wouldn't use it.