The red spots are common, especially as newbie. When doing dry jelqs it’s entirely reasonable to use one hand for a certainly number of strokes then swap to other. As long as you kegel between jelqs to maintain pressure. With wet jelqs the alternating hand strategy tends to make more sense to me. Being that you’re a newbie, I’d recommend waiting for the red spots to clear up then starting again. As long as your penis feels fine that is.
300 jelqs in 20 minutes isn’t overdoing it in my opinion. Consider that the newbie routine calls for 200 jelqs in 10 minutes. Spreading jelqs out over 20 minutes would indicate to me that you were putting less strain on your unit than you would have been if you had have used only 10 minutes for the same number of jelqs.
Again, if your unit is feeling fine aside from the red dots, wait for them to subside and get back into the newbie routine. The more accustomed your unit gets to the exercises, the less you’ll see the red spots.