I felt like my mind had catapulted into chaos at that moment because I had left my job and broken up with my partner.

"broken up" on its own brings to images something physically coming apart. I think it's a little more natural to specify a bit more here to avoid that.

My tTraveling eExperience.

A title doesn't usually have a period at the end. This one is not a complete sentence, so it definitely shouldn't have one.

At first, I didn't know why I had chosen to take a long journey on my own.

Also good: to go on a long journey alone.

I felt like my mind had catapulted into chaos at that moment because I had left my job and broken up.

Most readers will probably infer that "broken up" means ending a relationship, but it sounds slightly incomplete. An option would be to add a little more info, such as "with my ___." On the other hand, the terse, abrupt statement fits well with the situation of being catapulted into chaos.

I was completely exhausted, physically and mentally.

An optional comma lets the reader absorb the information better.

However, these experiences taughtgave me a strong sense of achievement and fulfillment.

I think "gave" works better here. I'm not sure a sense of achievement and fulfillment can be taught.

In addition, traveling to numerous countries has, by far, taught me the greatest sense of composure and adaptability.

The phrase "by far" is a little awkward here. I think setting it off with commas helps.

Another option is to delete it:

"In addition, traveling to numerous countries has taught me the greatest sense of composure and adaptability."

A third option is to use different phrase earlier in the sentence with or without "I have done."

"In addition, more than anything else [I have done], traveling to numerous countries has taught me the greatest sense of composure and adaptability."

I felt like my mind had catapulted into chaos at that moment because I had left my job and brokenwent through a break up.

We live and we learn through thatsuch real-life experience(s).