I want to hang my plant but my ceiling is concrete. I don't have a drill. I have a hammer and screwdriver.
I think that you CAN use most types of fasteners usually installed with a drill but such would be unreasonably difficult! You could get a Tapcon™ screw and hit it with a hammer enough to cause a small hole, then use the screwdriver to turn it endlessly until it drills its way into the concrete. That would wear out a number of screws and take days - unreasonable!
Consider taking a piece of 4” 1x4. Use a “cup hook” - turn it by hand into the wood* - this will hold the wire or string from the planter. Draw a pencil outline around the piece of wood on the ceiling. Then sand or scrape the area until all paint or coatings are gone, and the surface is a little roughened up. Use an epoxy to attach the wood to the concrete. Use tape, like gaffers or moving tape, in several long strips to hold the wood in place while it sets. After epoxy sets for (usually 24 hours - see the label) you can hang the plant. Bigger, heavier plants may need more glued surface area. Eventually, depending on the concrete, this may fail, but it should last a long, long time!
*the screw from the cuphook could split the wood when you turn it in without drilling the right hole first. If it does, try another piece of wood, it’s a piece that’s normally ‘scrap’ sized, easy to find for free, and one or two tries should do it. Once epoxied, even split wood should hold up a medium sized plant....
A hardened masonry nail can penetrate and hold in concrete... but concrete has low tensile strength. The nail might hold in a concrete wall or floor, but in a ceiling, it would likely cause a spall - a big divot - if any weight were suspended. Pre-drilling the nail hole would give a better chance of it holding.
Use the nails with caution! Wear eye protection, because hardened nails (and concrete) can shatter explosively. Also, hold the nail with a tool to avoid smashing fingers. See this video on their use.