Seeing a dietitian is a great idea, but until you do I'll offer the following advice:
Start strength training to build some muscle. In my non expert opinion, while you are a little underweight your body looks to be carrying around the minimum amount of body fat so adding muscle to it will add shapely weight without increasing your size as much as fat (muscle is more dense than fat).
To that end, I'd focus on eating more protein (meats, eggs, cheeses, nuts, beans, mushrooms, tofu, etc). You might also try protein powders, bars, and shakes.
You can still do cardio and gain weight, but you'll need to eat more calories to make up for the calories you burn doing cardio. If eating enough is already a problem, you might try switching from 45+ min low intensity cardio like bike rides or brisk walking to 10-15 minute higher intensity cardio activities like jump rope or burpees. If you do want to do longer cardio, stop every hour or so and eat a snack to give your body the fuel it needs to keep going without burning muscle or fat.
