Should i fake this as a last desperate attempt to get him back?

me and my ex split up 3 weeks ago he finished it as he found textx on my phone that were innocent but he believes there not. he told me he missed me a week ago but then when i tried to get him to meet me he told me he wouldnt as he wasnt getting back with me. i need to know if he still cares, i got an idea in my head that if i told him i was really sick (or in hospital) i would really see how much he cares if it got to him or not, he would never find out the truth as we have a long distance relationship. would this be really bad? i love him and miss him and at least if i done it though i would know by his reaction if he cared or not. need opinions on this, please dont judge as im sure a lot of you have done something in a desperation