Just started cutting and I got a pec strain. Should I continue to cut?

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So I’ve been cutting for about a week and I’ve alreddy lost 6 lbs (water weight lmao), anyways I strained my pec while doing a back off set on bench today. I think that what caused it was not adequately recovering from my last session. I also did tear my other pec last summer, but it was strained for about a month on and off because I was a dumbass and would jump immediately back into heavier weights(that’s what caused it to finally tear). When it was strained tho, it would feel better after a few days. I also kinda really want to cut NOW because I’ve been bulking the last year and half and I added over 300 lbs to my powerlifting total while only moving up one weight class. I just feel really bloated and fat and I look pretty big in clothes but I’m not very lean. (I’m 5’6 and 184 lbs). I also don’t really wanna postpone it in a few weeks because I will have to cut into the summer and by then I will be traveling a lot and will not be able to maintain a good cut. I’m certain that I can train every other muscle in some way though. Will I be able to keep most of my chest muscle and heal properly if I have to miss training chest for 1-2 weeks?