I am sorry that you are not feeling well.
Every time when you notice something strange during an activity (like a push-up) that you have been doing regularly for a while, it is cause to stop and investigate. A sensation of ‘dizziness like a stroke’ must not be taken lightly, and while it may not have been the push-up itself that caused it, it may be the degree of exertion.
But whatever the speculation, I would go and see a physician as soon as possible. In the meantime, I would stop doing push-ups until cleared to do so again by your doctor.
I wish you good health.