Please check for grammatical errors

I can see nothing in terms of grammar that needs to be changed. There are a couple of places where your paragraph could be made stronger.

Your second sentence ends with two prepositional phrases, one after the other. There is nothing you can do to eliminate these prepositions without changing the meaning. However, you can avoid the strung together feel of the prepositional phrases by altering the structure of the sentence. This would also give the paragraph a bit more rhythm. Move "in April" to introduce the sentence --> "In April, she came ..."

Consider emphasizing "long time" by saying "such a long time."

Consider joining your fourth and fifth sentences with the conjunction "so".  The will help vary your sentence length and make the writing more interesting.  (When sentence length varies, the comprehension and interest of the reader improves.)

Consider simplyfing "as far as my knowledge is concerned" --> "as far as I knew".

Oh, I did find one punctuation error. You have a compound sentence toward the end that needs a cooma before the conjunction "and".

In addition to Jeff’s points, two sentences seem a bit off to me. 

I was glad to meet her after a long time.  It sounds like you are meeting her for the first time, but after a long time is somewhat unclear. Is it a long time since you last met her?  Was this an online class, so you met a long time ago and this is the first time in person? I was glad to finally meet her in person after such a long time. 

Besides, I was curious to see her quicksilver smile.  This sentence seems out of place.  Later, you mention that your understanding was that she always frowns.  If that is true, then how did you know she would be smiling and how did you know it would be a quicksilver smile.  This sentence is saying that part of the reason you agreed to meet her was to see that smile, which contradicts the later statement.  I had to look up quicksilver as an adjective in the dictionary.  In this sense, it means rapid or unpredictable in movement or change.  Does that describe her smile?   

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