Swimming

It rained heavily for two days because of the typhoon. I took THE train from Shanghai to Haining this morning. It was raining when I boardED THE trian(,) but it was sunny when I GOT off OF the train.
I felt very good. I AM going swimming with my friends this afternoon.
I called Tom(,) he is my university classmate. He workS in hangzhou. He is A hardware engineer in Haikangweishi.
He told ME that he would go to THE library and RETURN some books. But he SAID TO me(,) "LiHua is free this afternoon".
LiHua is a beatiful girl. She is Tom' co-worker.
I felt very shy because I have never swum with girls.
but Tom said to me(,) (")Lihua likeS swimming and she is a lovely girl.(") 
I was planning to send a message TO Lihua.
I WROTE(,) "Hi, Lihua, I am Gary(,) Tom's university classmate(.) I am going swimming this afternoon. but Tom HAS no time. He told that you like swimming. Can I call you to GO swimMING? How about you?"
Just THEN(,) my cellphone rang. I recEived a message from LiHua. He WROTE(,) "I HAD wanted to GO SWIMMING since LAST Monday but nobOdy wantED to swim. I think it is a good idea for us. What time are YOU going to swim? I will get to the swimming pool on time".
I feLt very happy but I had to buy A swimsuit and swim cap.
I believe it WILL be a nice time for us.
Thanks

Swimming

It rained heavily for two days because of the typhoon. I took a train from Shanghai to Haining this morning. It was raining when I boarded a the(use 'the' now because you mentioned a train earlier and you are still writing abou the same train) trian train. But it was sunny when I got off the train.
I felt very good. I was going to go swimming with my friends this afternoon.
I called Tom, that he is was(use 'was' because you aren't in university anymore. That was in the past.) my university classmate. He worked in Hangzhou. He is a Hardware Engineer in Haikangweishi.
He told me that he would go to a library and give back some books. But he told me, "LiHua is free this afternoon".
LiHua is a beatifull girl. she is Tom's co-worker.
I felt very shy because I have never swum with girls.
but Tom said to me, "Lihua likes swimming and she is a lovely girl." 
I was planning to send a message for to (use the word 'to' because you want to send a letter to Lihua. You use the word 'for' in this situation if you are the person helping Lihua send a message to someone) Lihua.
I writed wrote "Hi, Lihua, I am Gary. that I am Tom's university classmate, I am going to swimming this afternoon. but Tom have has no time. He told me that you like swimming. I can call you to swim._How about you it?"
Just for a mommet, my cellphone rang._I received a message from LiHua._She writed wrote "I wanted to swim since next last(I chose to replace 'next' with last because you had the word 'since' preceeding the word 'next'. When you use the word 'since' that means you are talking about a past event.) Monday, but nobody wanted to swim. I think it is a good idea for us. What time are you going to swim?_I will get to the swimming pool on time".
I fetllt very happy. but I had to buy a swimsuit and swim cap.
I believe It would will be a nice time for us.
Thanks

Here is an alternate way of writing your second to last sentence: "I felt very happy; however, I had to buy a swimsuit and swim cap." Notice how the word "but" can be replaced with the word "however" with the addition of a semicolon prior to the word "however" and a comma after the word "however". ";however,...etc".