In this case, your first option is to see if you can make a special arrangement, on account of your allergy, to immerse in the salt water mikveh.
If that is out of the question, you could explore the possibility of immersing in a natural body of water, if this can be done legally and safely. Please see our Q&A about immersing in a natural body of water and get back to us with any questions.
A third option would be to arrange to immerse right after water is changed and before it is treated with chlorine.
Choosing not to immerse is an option, but means that the niddah prohibitions will remain in full force. Dipping in the bathtub is not a halachically valid immersion and does not change a woman’s mikveh status.
Please get back to us with any further questions.