Is it safe to use Minoxidil at night and then wash my hair in the morning?

Hi there, using minoxidil over the course of a night and washing your hair in the morning should be no problem. I would caution against over shampooing your hair as this can ultimately hasten hair loss and damage your hair. 

While minoxidil works for some, the problem with the medicine is that
it does not stop hair loss, and the DHT will continue is binding to the
hair shaft which will eventually overtake any additional growth caused
by the Minoxidil and die, perhaps just slightly later than it would have
without the medicine.

Also, the alcohol base required to support the active ingredients
also cause irritation of the scalp and severe reactions for many people,
such as the increased shedding you are describing. The fact is that it
does not work for everyone.
The best thing to do would be to see a doctor who specializes in hair
regrowth and the re-balancing of body biochemistry who can diagnose the
cause of your hair loss. Good luck on your search.

What you have described should be fine. Ideally minoxidil is left on for 8 hours as the 'minimum' time.
This advice comes from a 1990 study. In that study, twenty-two healthy male volunteers completed a four-way, multiple-dose, randomized crossover study to determine the relationship between contact time of applied drug on the scalp and minoxidil absorption from a 2% topical solution.  The researchers examined how much minoxidil is absorbed at 1 hr, 4 hr compared to 11.5 hours. Relative to the amount absorbed after a contact time of 11.5 h, absorption was approximately 50% complete by 1 h and greater than 75% complete by 4 h. Minoxidil therefore should ideally be left on 8 hours or more. What you have described should offer benefit.
Reference
Ferry JJ et al. Relationship between contact time of applied dose and percutaneous absorption of minoxidil from a topical solution. J Pharm Sci 1990 Jun;79(6):483-6.