I have fixed a 30 years fixed mortgage rate at 4.5% last month with a one-time right to exercise a float down.

Locked in at 4.5% last month? If you can float down to 4.25% at no cost I certainly would. But 4.5% (even last month) is pretty high --- Ii would highly advise getting at least one other quote.

Yes! Rates dipped a little in the last few days. Take advantage of it while you can.

I would before rates start going up even higher.