Insect eggs

Yesterday I was horrified to find a cluster of small white/cream eggs on the underside of a newly transplanted pepper. I picked the whole darn leaf off and threw it away. I get totally grossed out by insects.

after some research ( double gross ) I am now wondering what they were. They looked same shape as the squash bug eggs but they were not red /orange/brown.
I have come across 2 pictures of eggs that are similar. One was a Monarch butterfly egg , but they dont lay eggs on Peppers! but..... i had one hovering around that pepper plant for 2 days.
The other option is lady bug eggs.... hope they weren't those. Haven't seen any lady bugs around though.

Another problem today. BIG problem. I have a gigantic burning bush at my back gate. Need to trim it as we can't get out haha. Today I noticed that all the new growth at the tips is curled over and covered, I mean COVERED in black aphids.

Sometimes I really hate gardening.

I have a terrible time with ants on my burning bush. Yesterday I looked really close, and sure enough there were aphids all over it, which is probably why the ants were always there. Sorry I can't help with your bug egg problem. All I can say is keep your eyes peeled and try to keep the eggs picked off the plants. You might consider buying a bug reference book so you can easily look up what the bugs/eggs are and decide what to do with them.