160 is rather high, but I suppose not out of the realm of possibility. When you lay in a hot bath, your heart will begin to beat faster in a futile attempt to cool your body down. I would say what you're experiencing is a common (although on the high end) reaction to being immersed in hot water. Personally, I hate baths. It's like you're sitting in a stew pot of your own filth.
Your breathing affects your heart beats rhythm. Interrupted respiration, not getting enough oxygen-as in a sinus blockage-can affect the heart, causing it to palpitate with quite uncomfortable force. OK-no sinus condition? Any internal blockage in the respiratory/circulatory system triggers a speeded up heart response. Have both checked including ENT for esophagus and tonsils. It's probably nothing that serious. Good luck.