Good news about the pump!
You can safely add enough chlorine tonight once the pump is going to bring the pool to shock level and probably lessen the green stink at least, although shocking really does require a test kit. You can wing it if you've got a pool store handy to do testing, a friend or neighbor with a FAS-DPD test, or if you're willing to do some creative dilution with an OTO chlorine test kit (assuming you have one). Once you get your test though, you'll realize how in the dark you were while winging it.
Since you have not added anything yet, we can assume there is no CYA in it. You're going to need that to be around 70ppm once you get the SWG running, but for now only add enough to get to 30, maybe 40ppm (Texas, right?). Tonight, you can add bleach to shock level for 0ppm CYA (use pool calculator for your volume - you're going to be aiming for 10ppm). Tomorrow, add the 30-40ppm CYA in a sock and when it's all dispersed, then assume you have the amount your intended to add (if you calculated properly - measure your water depth - don't rely on mfr's gallonage estimate) and follow the CYA/CL from pool calculator for an adjusted shock level (it'll be higher than 10ppm but it depends on CYA).
Plan to run to the pool store a couple times tomorrow for testing if you do decide to begin shocking. You want to maintain shock levels all day, but sunlight will burn it all off without CYA so do get that in that right away.
Walmart's CYA (stabilizer) disperses rapidly, and often shows on a test before a week has passed but don't bother testing that till you're ready to add more CYA and start the SWG. 30-40 will be fine for now and will save you a little on bleach.
