I'm scared I won't lose fat in time for summer

I'm a 5'9 woman who was skinny her whole life up until my first year of college where I gained my freshman 15, and now that I'm a sophomore I still haven't lost it, and honestly for the most part I hate how I feel in my own skin. Especially looking back at old pictures and videos of myself. I used to weigh 165lb (sometimes more sometimes less). At this time I was playing volleyball and basketball, ate at specific times (because I was in highschool) didn't eat super frequently until I got a real job where I had the money to buy whatever meal I wanted, as well as a boyfriend who loves going out to eat. Since starting college, I'm now 183lbs. I've become more aware of my eating habits though, unfortunately I had to learn the hard way. I have a very busy lifestyle with me being a full time student and working at a hospital part time etc etc, but I REALLY want to lose around 15-20 lbs as fast as possible.

My birthday is next month and I'm already dreading it bcs I don't really like how I look anymore, and summer is on three months. But there's still time and I'm hoping maybe somebody can give me some good advice.

My biggest issue is finding the time to work out/ folding motivation to do so. I don't feel comfortable going to the gym due to my insecurities but I have dumbbells and resistance bands at home, along with a waking pad so I'm looking to just start there. I also try to take around 10k steps daily.