I had a very similar problem when I was younger.  I was 5ft 2 inches and only weighed 37kg.  My problem came from a lack of eating due to me having just moved out of home and trying to keep up with my studies.  It actually got quite dangerous and I was threatened with hospitalisation.

I was told to eat foods that are higher in calories, no low fat foods at all.  I had to eat every 2-3 hours and the foods had to be really filling.  I ended up going through a whole loaf of bread everyday by myself.

With any weight issue, you have to take into account your height.  For me, my ideal weight is 55-60kgs, and even after having just had a baby, I'm probably a little on the lighter side of things and need to start eating more again.

Your body mass index is important to know.  That is your height, weight, fat/muscle ratios.  To get these, you should see your doctor and ask for help from them.  I feel that you are way to light for your height, even though you haven't given it, as by your age, you should be more than that.  You currently weigh as much as I did when I was about 13.

I have to wonder if you don't have an eating disorder though, whether by choice or by what I had, which was a lack of interest in food due to trying to keep my life together.  There are many forms of eating disorders that are recognised now, and mine was (and still is) a stress reliever type.  That is where someone ends up stressed out to the point they skip meals in order to keep going with their daily routine.  This can be very dangerous, and is the hardest eating disorder to diagnose.

Obviously, I was still told to eat healthier foods as no one recommends a diet of just cake and junk food, but I was encouraged to increase the amount of less healthy foods as well, as long as I kept a balance.

How tall are you is another thing to take into consideration also.  I am 4' 9"  and I weigh 83 pounds so becasue I am so short I am ok.  I just eat everything and I don't gain weight

You could try to increase your intake of carbohydrates (potato, rice, bread etc). Also try adding the powder 'Sustagen' to your milk. You can get milk drinks that are meal replacements for people who are dieting - but you could drink this on top of your normal diet... Go to the chemist and find out what's available. Also try eating larger meals and more frequently. This has got to be more enjoyable than trying to lose weight!!!!!!!!!!!!!!

I would advise that you speak to your doctor if you can.  They may be able to give you good advice about what foods will help you gain weight, or help you deal with any issues you have that may be preventing you gaining weight at the moment e.g. metabolic issues. 

Stay with a healthy diet. I don't know what your diet consists of now but I am working with a family that is from India now and they are very small and find it hard to put on weight too. They are vegetarian and eat a lot of dahl, rice, chipati, etc. They are still healthy and not sick often. Maybe try to eat more regularly. 38kg is a low weight, but what is your height? A friend of mine who had trouble putting on weight was told to eat bananas, yoghurt, I can't remember what else sorry as I have not had that problem myself. There are special milk drinks too like pediasure but not sure what you have available in your country. Hope this can help and you get some other suggestions too.