Hello there! I am 20 years old and about a year ago I started seeing very red stretch marks appear on the inner and outer parts of my thighs. I have gained about 10-15 pounds. But altogether I am only 5' 2" and 130 pounds. Which seems about average for a girl with my body type, size, and age. So why am I suddenly seeing these stretch marks appear? They are making me very self-conscious. If anyone may know a reason I suddenly have stretch marks, or how to get rid of them, please let me know! Thank you!

130 pounds for someone your age and height is a perfect weight, so don't worry about that. There are a number of reasons you may be getting stretch marks.
Stretch marks normally appear in times when the body is changing, primarily during adolescence or pregnancy. They appear because the skin is literally 'stretched' because they body changes shape or through weight gain. Some adolescents, especially girls but sometimes boys too, can form stretch marks even if they don't gain weight because they're hips and breasts are becoming more prominent and it happens too quickly for the skin to accommodate it correctly. Again with pregnancy, it happens because the stomach and breasts swell at a faster pace than the skin can accommodate.
For you, I can only imagine that you're suddenly getting stretch marks either because of the weight you mentioned you gained, so although you are not overweight, your skin hasn't been able to adapt to the change quick enough.
A main point I would like to stress is not to worry, more people have stretch marks than you would think. I started to get stretch marks when I was about 14 around my stomach, inner thighs and breasts. I'm only 21 now and although at the time they were very angry and red, they are now virtually invisible.
Stretch marks will often fade to a thin silvery line, or will disappear completely, all by themselves. But if you're conscious about them now, there are some products on the market that can speed the process along. One product that I've always used is called 'BioOil'. It comes in a white box with orange writing, and the bottle is clear with a white lid and the liquid is like an orangey colour. It's actually advertised as a way to reduce the appearance of stretch marks and scars, and has been a massive help to me for this and as a general intensive moisturiser. It's around £12-13 a bottle, but lasts for ages because you only need to rub in a couple of drops daily.
Any doctor, at the moment, will tell you to wait and see if they disappear by themselves, which they most likely will. But if it gets to the point where a couple of years have passed and they are still red and angry (very unlikely I might add), laser treatments will be available for you to reduce their appearance.
All this said, I don't want you to worry, because like I said, they are extremely common, and will most likely go away on their own :)
I hope this has been helpful to you.