You Coulomb / Ah calculations look about right, but there is not much point in bothering with Coulombs. You could just work in Ah.
Your phase "22mA every second" is a bit meaningless. If you are getting 22 mA, then that doesn't depend on the how long it has been running for.
Also, if you are getting 22 mA at 1.5 V, you can't charge a 3.7 V battery at 22 mA with that. You would need a boost regulator or charge pump or something to bump the voltage up to more than 3.7 V, and that will cut the current down to less than about 7 mA.
Also, Lithium batteries have a maximum voltage of 4.2 V, so you have to allow for that.