Q.Starting seeds
A friend told me about using egg shells to start seeds and it seemed like an easy thing to do so I just went for it. Unfortunately, I didn’t even think to wash out the shells before planting the seeds. Some of the new vegetable plants are doing amazing! Should I be worried about salmonella in the shells?

It's great that you're using eggshells to start your seedlings and that they're doing well! Yes, the shells should have been washed prior to being handled but once you plant your seedlings the eggshells will eventually decompose into the soil. To be on the safe side, wear gardening gloves or even latex gloves when you get ready to plant them in your garden.
Here are some articles that may also help you:
https://www.gardeningknowhow.com/special/children/growing-seeds-in-eggshells.htm
https://www.gardeningknowhow.com/composting/ingredients/eggshells-in-the-garden.htm