Can I get a work permit after my H1B expires and stay legally in the country after we marry while we wait on a waiver?

I participated on a program sponsored by the US government and came to the country on a J-1 visa. I am subject to the 2-year rule and spent only 3 months in my country before coming to the US to do a Master's. I graduated last year and got a job in the US. I just got an H1B visa and will be able to adjust my status from F1 to H1B, although I can't leave the country and come back because I don't have a waiver to get a visa stamp. My boyfriend and I are planning to get married in a couple of years and we think we might be able to qualify for a waiver for extreme hardship because he has some mental health issues that have improved since we started dating and the impossibility to keep his treatment in my country could be a problem for him to move to my country with me. Does the fact that I have this barrier will keep me in a limbo in which I will have to wait until a waiver decision to be able to adjust my status a get documents to allow me to work? Does anyone have any advice?