False lashes poke your eyes mainly because of two reasons: The lash band is hard and made from plastic or is coated, or the lashes are not trimmed and too long for your lash line which results in the band poking the inner eye and making it uncomfortable to wear. Which happens often and if you're a newbie to lashes, you may stop wearing false lashes because of the poking.
Feel the lash band and see if it's soft. The soft lash bands are usually made with soft cotton or cotton elastic which is the best. Then trim your band, (many people do not trim the band) the band should not pass the outer part of your eye and the the band shouldn't lay in the "inner' part of your eye, which is where you feel the "poking". Trim the band so the band lays before the inner eye where your own lashes end.
Try these tips and they should help, you may have to try different brands or styles to see which is the most comfortable. Ideally, false lashes should be comfortable and shouldn't poke you.
Above lash is Koby Mink Lash