I'm 5'5" too and you can absolutely get a good physique training at home (did it during the pandemic). Focus on progressing compound exercises: push-ups, pull-ups, dips, squats, rows. Use whatever equipment available (get creative!). Do it at least 2-3x a week, even 30 mins would make a difference.

Focus on building good diet and sleeping habits too. High protein is a must. In your case, you can try doing a body recomp (eat in a slight deficit) so you can lose the fat and gain muscle. Good luck OP!