Praise be to Allah.
Bursting pimples that appear on the face does not invalidate the fast and does not require that day to be made up later on.
The things that invalidate the fast are well known and are indicated by the Holy Qur’aan and the saheeh Sunnah of the Prophet (peace and blessings of Allaah be upon him). They are as follows:
3-Eating and drinking
4-Things that take the place of eating and drinking, such as injections that provide nourishment
6-Cupping and things that are akin to it, such as donating blood
7-Menstruation and postpartum bleeding in the case of women
For information on the evidence for the above, please see question no. 38023.
It is not permissible to say that this thing invalidates the fast without sound evidence to that effect, and there is no evidence that busting pimples or boils that appear on the body invalidates the fast.
Based on this, your fast is valid and you do not have to make it up, but you will be rewarded for the day which you fasted to make it up, and that will count as a naafil (supererogatory) fast on your part.
It should also be noted that you should refer to a doctor about bursting these pimples to find out whether it harmful or not; if it is harmful then you should not do that.
And Allaah knows best.