Actually the opposite! You'd be able to wear one fine and you'd find it doesn't fill up as quickly either! Even with heavy flow you can wear it up to 12 hours, if it happens to get full sooner just empty it sooner. Tampons hold no where near as much because they are just an absorbent piece of whatever material it is they're made from, whereas the cup is simply a container. It'll hold any clots easily as well as the regular flow, and you simply empty it, wash it, and use it again! No more tampons or pads in the purse, no more wrappers and no more having to re-stock your supply.
Mine's a DivaCup https://www.divacup.com/ the two sizes are 1. for women who have not given birth and 2. for women who have or are over 30. I will never go back to tampons or pads!!