Sometimes I hadget a terrible headache after drinking it.

I corrected headache. I added get as had is past tense

Since then, I've calm down my headaches have calmed down.

This is good I wrote another way to say it

When I had troubles by no space keepingno more space for the books, my brother recommended

I made sound more natural

Sometimes, I hadwould get a terrible headache after drinking it.

My friend saiuggested that I should try tea forto improve my health.

Since then, I've calm down my headachemy headaches have gone away.

When I had troubles by no finding space to keeping the my books, my brother recommended that I should try reading e-books.

Some minor edits for clarity.
I think your sentence got cut off here, so I added the fragment from the next section.

So I started reading them on the Kindle app.

Since then, I've been buying and reading lots on manythings on several other e-book apps.

Nowadays, reading e-book iss are more convenient than paper books.

Practicse Tense

Practise is the verb

Sometimes I hadve a terrible headach after drinking it.

Since then, I've calm downdecreased my headaches.

Nowadays, drinking tea is one of my favorite hobbiethings.

When I had troubles byfound I had no space keepingto store the books, my brother recommended

Nowadays, reading e-book is more convenient than reading paper books.

Sometimes I hadwould get a terrible headache after drinking it.

Your original sentence is fine, this is just a stylistic suggestion to use a more commen phrasing (in my opinion).

Since then, I've calmed down my headaches.

Because you "sometimes" "used to" get a headache it means you got it (them) multiple times. So you should say "my headaches" (plural) even though its okay to say "I used to get a headache when ______" (English plurals are so weird, I know ㅠㅠ). Just remember that the "sometimes" and "used to" part means it happened more than one time, so you need to say "my headaches" (plural) here :)

Also!! You can say "Since then, my headaches have calmed down." Your sentence is totally fine, but personally I would write it in this form instead, just because it sounds nice to me. You can keep your original sentence if you prefer it! ^^

When I had troubles bydue to having no space for keeping the books, my brother recommended

You can say "due to" or "because of" or even "caused by" here. They are all roughly the same in this situation.

You can also say: "When I had trouble (with) finding space to keep the books in, my brother..."

Nowadays, reading e-books is more convenient than paper books.

You can say:

1. reading e-books is more convienient...

or

2. reading an e-book is more convenient...

Just choose whichever one sounds nice to you, or flip a coin :P You just need to either write "e-books" in plural form, or say "an e-book" (singular) for it to sound natural. The meaning will be the same either way.

Sometimes I had a terrible headache after drinking it.

My friend said that I should try tea for my health, so I started drinking it every day.

Since then, I've calm down my headaches have calmed down.

Nowadays, drinking tea is one of my favorite hobbiesthings to do.

I wouldn't really consider drinking tea a 'hobby' though others might disagree.

When I had troubles by nowith running out of space to keeping the books, my brother recommended

(This was a tricky one, I think my correction works)

Nowadays, reading e-books is more convenient than paper books.