Based on my understanding, the sentence should be written as either:
1) Ich habe angefangen, zu reisen.
[The infinitive phrase is placed at the end, separated from the main sentence by a comma.]
2) Ich habe zum Reisen angefangen.
[The infinitive phrase is replaced by a noun phrase "zum + Infinitiv", and it is placed before the ending verb term (past participle).]
"..und mich währenddessen immer hab ablenken lassen"
"hab" is the imperative Du-form of "haben", and thus I do not understand why it is put in an indicative sentence.
In general, however, the German structure is as follows:
1) in a main clause, the conjugated verb is always placed at the 2nd position;
2) in a subordinate clause, the conjugated verb is always placed at the end position.
Ich wünsche Dir einen schönen Tag.／I wish you a good day.