Old linoleum floor

Hi there! I just tore up some carpet in my bedroom and there is old linoleum underneath. It's not in my budget to cover it which is my long term goal. So I decided to paint it for now. After doing a few rows it dawned on me that it might peel off easy if furniture..... like a vanity chair is slid back. I will put some kind of floor protector on bottom of bed and chairs. So I don't even know if I want to take the time to paint all the rest if it's going to peel. My hope is once it cures it will stay on🙏. Also my daughter suggested a clear coat??? Would that help? Any ideas. I did not prime it😳 I just used a high quality paint.