I have rashes/acnes with white liquid (pus?) which can be easily popped on my chest and neck which appeared a week after taking doxycycline for an UTI

Doxy can cause a. sun sensitivity that can lead to blisters or rashes on sun exposed skin. I would not pop blisters as they are sterile and there is less risk of infection. Try using aquaphor or vaniply and see a derm to confirm or refute diagnosis.