My mom walked in on me and my girlfriend cuddling and now she thinks we're having sex?

Today around 7 or 8ish, my girlfriend was over and we were both just kinda laying down in my bed and it just so happened that my shirt was off, she was wearing a tank top and was in a pair of my boxers because she didn't wanna be in her jeans all day. she's comfortable with me seeing her In a tank top but that's it. anyway, nothing was happening because she's shy and I didn't wanna make her do anything she didn't wanna do. All of a sudden she scooted over and laied her head on my chest and it made me feel good knowing that she was comfortable enough and I felt like she trusted me and I was doing my job as being a good boyfriend. I know it's a lot to get out of one moment, but considering how shy she is, it was pretty big deal :P anyway, she took one hand and it was resting in between my neck and my shoulder and she took her other hand and held my hand with hers. Then she kissed me in the corner of my mouth and that's an even bigger deal since she's never kissed me before let alone that close to my mouth (though ive kissed her plenty of times on the forehead and cheek and stuff) and then she brought up our hands and kissed the back of my hand... I asked her where all this was coming from all of a sudden and she said she just wanted to show me how much she liked me for a change. I didn't reply to it, and maybe about 5 minutes later we were still in the same position and the kissed me again but this time on my lips and then after that for a while she started moving down and kissing around my jawline headed towards my neck and just at that moment my mom walked in and she saw that I was shirtless and my girlfriend wasn't really wearing that much (the heat was up pretty high so we were both really hot) and she told my girlfriend to get a shirt on and for me to get a shirt on and to downstairs so she could talk to us and she shut the door to let us get dressed and my girlfriend was already turning red and so was I and we eventually went downstairs and she said that we're not allowed to see each other anymore be because she obviously thinks were having sex but we're not and she doesn't believe me what could I do so that we could see each other again because that's not fair and my dad doesn't care but she still won't listen to anybody please please help i wanna see her again, and chances are, she's not gonna open up like that again in fear that my mom will walk in, so if that does happen, how could i encourage her to do that without making her feel peer pressured or uncomfortable? btw i just turned 15 on the first and she's 14