Sure, conjugated estrogen can trigger hair shedding a few weeks after starting. It does not happen in everyone but it's a recognized side effect. Shedding may subside (over time) in some users.
If one stops minoxidil after two months, there might be a bit of shedding. Shedding can always speed up underlying genetic hair loss (if present) but after two months this effect should be minimal. If you are not comfortable with a medication it should be stopped. If however, you are not sure of...