Summer has begun

The summer's rages have come and a lot of people will get tanned. I just went to the beach and forgot to protect with sunscreen, so I almost had burned my back. Next time I won't forget this lesson, that's for sure.

The corrections from the other tutors are also correct. I am from the USA, by the way. There are many ways to convey one message, so my hat off to everyone here! 

I'm from a beach community in San Diego and we use the words "sunscreen" and "sunblock" interchangably. Alternatively, instead of "cream" we would say "sun tan lotion". 

As for the titles capitalization of "Begun", I'm not too sure but I think Amelia has got it right with regard to the title of a written text.

Summer has began begun

The sSummer's rages have comes and a lot of people will became (better: are going to get) tan. I just went to the beach and forgot to protect with creme (sunblock) so I almost had burnt my back. Next time I won't forget the lesson that's for sure.

Good! That's an important lesson. :)

Summer has began Begun

The summer's rages have come comes and a lot of people will became get tan. I just went to the beach and forgot to protect myself with creme sunscreen so I almost had burned/burnt my back. Next time I won't forget the this lesson, that's for sure.

Well done! I wanted to point out a couple of options. Sunscreen and sunblock mean the same thing though sunscreen is more common in my area. Also, I believe that burned is more commonly used as the past tense of burn in American English, and burnt is more common in British English.