Are these sentence correct grammatically?

有一天，妈妈让我把房间打扫一下。我先扫地。扫完地以后，我把桌子和椅子擦了擦，也把书架上的书整理。整理完书以后，我看一看，窗台上还有几张纸。我觉得把这些纸也理了理。我正在把这些纸的时候 ，忽然发现了那人还有一个东西。” 奇怪，“
我想，“ 这是什么东西？” 我靠近些，才发现这就是我的驾照！两个月前，我到处找它，可是找来找去都找不到。

“妈妈，你猜我刚找到了什么？是我的驾照呀！”

听到这好消息 , 妈妈也高兴极了，说： “你总是乱放东西，以后不要丢三落四。”

There's no need to leave spacing between Chinese words, since each character is a complete word in itself. 

有一天，妈妈让我把房间打扫一下。 -- Did you really mean to say that your mother let you clean your room? Not wrong, just odd. My mum always nagged at me to clean my room, lol.

我先扫地。-- Again, not wrong, just odd. Sentences just aren't this short in general, and especially not in writing. 

我看一看 -- literally means to take a look, and has the additional nuance of purposeful action. I think you were trying to go for more of a casual glance around the place kinda thing, so the nuance is a little off. Try '我注意到' instead, meaning 'I noticed [that]'.

窗台上还有几张纸 -- You had "一些" there before, which is too generic. Chinese uses '张' to number thin/flat objects like paper.

我觉得把这些纸 -- '觉得' has to do with feelings or inclinations. In this case, it would translate to, 'I felt to put these papers in order'. Notice how the grammar is a little iffy too; it's just weird phrasing. Perhaps you were going for 'decided', '觉得', instead?

理了理 -- Not sure if this is wrong or not, tbh. Sounds weird though. I'd stick with '一' to be safe.

我正在把这些纸___的时候 -- looks like you're missing a few words here. 

忽然发现了 -- excessive use of '了'. '了' usually just places the event of a sentence in the past tense, but it isn't always necessary since Chinese tense itself is largely contextual.

那人 -- who? Did you mean 'over there', as in referencing a location? --> '那边'

还有一个 -- okay, now the '一's are getting excessive. If this were a composition in school, it'd look like you're trying to fulfil the minimum word count requirement (yes, I've been there).

东西 -- 'thing'. Not wrong, just very vague and not very sophisticated.

suggestion: 忽然发现那边还有什么东西呢！-- yeah, I've got no good explanation for this other than that it just sounds more natural. There is no English equivalent, just that having the '什么' there carries over the idea of an unknown object better than just leaving it as 'thing'. '呢' is an interjection. Means nothing, but adds flow I guess?

两个月前，我到处找它，可是找来找去都找不到。-- Had a lot of commas in there which I edited. Just like English, you don't want to pause too many times.

你猜我刚才找到了什么？-- '刚' works just as well on its own, as does "刚刚'. '刚才' sounds a little stiff.

是我的驾照呀！-- added words for better flow. '呀' is simply another interjection commonly used in speech.

说：-- pretty sure Chinese speech is distinguished from the rest of the text by a colon in addition to the quotation marks. (At least, that's how I was taught in school.)

东西？“<font color="#000000" style="background-color: rgb(255, 255, 0);">。</font> -- No need for extra punctuation after closing a section of speech.

你总是乱<font style="background-color: rgb(255, 255, 0);" color="#000000">放</font>东西 -- not wrong, but I usually hear people use 'toss', '丢／扔', instead of 'put', '放'. I'm guessing it has to do with the additional connotation of carelessness in throwing or tossing.

<font color="#000000">Good job overall. Don't worry about the wall of text I just dumped on ya, I'm just very nit-picky.</font>
It's cool you're learning Chinese, keep it up! 加油！