Oh, dear. I am sending you good thoughts... This is just like something I would do..
Did you place these clothes in the dryer? If so, I will tell you, this is going to be lots tougher to get out. Probably not going to ever totally come out.
All of those "spots" need to be treated like grease.
You also will really need to clean the dryer and washer drums to make sure there is no residue left. Clumps of chapstick could have collected in there or smeared around.
The tissue idea is good, you can even use newspaper to place between the clothing..
Use baby powder on each spot, sprinkle it on both sides of the clothing. lightly pat the powder onto the fabric. Let this sit for 4 hours, brush off the powder with a toothbrush and do this again until as much of the spot is gone. This may take a few days.
Once you have as much off of the fabric, treat with a spot cleaner like shout, or use straight detergent on each spot on both sides. Use the toothbrush to lightly agitate the detergent into each spot, both sides of the fabric. Let this sit for about 10 minutes, then wash. Look at your clothes before you put them in the dryer. Make sure they look cleared of spots.. If they are still there, try all of this again.