Unfortunately, I too have had this experience. I was diagnosed with breast cancer at 40. My quilt was about a generous lap or small twin. It was large enough to go from my chin to cover my feet. The chemo drugs aren't warmed before you get them and you can get so cold!! But my infusion center did not have any restrictions. They said I could bring whatever I wanted that would make me happy!! A bag is a great idea to carry it in!! And then you can put your stitching in it as well. I would sit and bind quilts during my 6 hour chemo sessions. So I was doubly warm!!
Next month is 4 years cancer free for me!!