Messy eater

My DS is 10 weeks old and milk gets everywhere when he feeds. We've tried so many different bottles and he still gets milk dripping and sometimes even shooting out the sides of his mouth. We have to wrap burping cloths around his chin and neck to soak up all the milk because it's too much for a bib to catch. Even while breastfeeding I have to put a cloth under his cheek. Did anyone else have this problem?