Then, the good news is, you still have beginner gains to make. My advice is (and this worked for me) -- don't 'bulk' or 'cut'.
- Clean up your diet (if you don't know what this means, read)
- Maintain a slight deficit
- Follow a good strength training programme, lifting 3-4 times per week
- Keep on doing some occasional cardio if you wish (and can manage)
Because 'bulking' will make you fat. You clearly feel unattractive (you said that you feel 'skinny fat'), and bulking will only exacerbate the issue. You train for yourself, so make yourself happy.
If you were to 'cut' you'd drop the fat, but you'd probably feel small in the process and end up feeling unhappy again. (this was the story of my life)
Why should you do the above? Merely cleaning up your diet and maintaining a slight deficit (and I mean 200-500 calories max) will set you up for steady fat loss -- you'll be a changed person 2 months from now. BUT, you should train with the intent of building muscle, as it is possible for your body to build muscle and drop fat at the same time when you're just getting started (think of it as the initial adaptations to actual difficult exercise -- take advantage of it because you can't do both at the same time effectively once the honeymoon phase is over). If all goes well, you'll be adding strength and muscle and uncovering it at the same time.
Don't make the mistake of undereating and doing too much cardio (this is why I said no 'cut') -- you'll ruin your metabolism over time and feel skinny.
Lift, build strength/muscle, eat a clean diet with a slight deficit.
Congratulations on the weightloss thus far. The physique you want is within reach.