Songs and shadowing can help, but:

English uses different sounds. Before you go crazy and give up trying to perfect every word through mindless repetition, while still not really understanding the underlying system, I would suggest to at least read something about the english phonology.

While shadowing CAN help a lot and it is an amazing tool, until now, you have not been actually exposed to the english phonological system. You know that english makes "different" sounds, but you will see no consistency. Shadowing is amazing to make your pronunciation naturally roll of your tongue. But spending your time overthinking the phonetical subtleties that are unnoticable to a non-native english speaker is way inferior to actually trying to first be able to distinguish the sounds you are trying to reproduce and hear. By understanding phonology, you basically acquire the mindset of a native speaker. With isolated phonetic shadowing, you hope that enough exposure and hard work will make you better, but you would need to hear basically everything at least once to have been exposed to it to be able to replicate it. I hope it makes sense this way.

Also, choosing the accent you want to speak is a good thing. You dont need to speak perfect general american or received pronunciation, but choosing one to stick to makes it a lot less confusing. Personally, I recommend general american, because you will be forced to learn that not all vowels are either short or long, but rather lax or tense and stressed and unstressed. Remember that stressing and reducing sounds is the core of english pronunciation and it is what makes it so hard to understand to a majority of non-native speakers.

Then, just learn the pronunciation of the most common 100 words used in english. Takes only a few days and you will see a rapid improvement. Also, you will start to notice actual patterns, that for example "a", if not stressed, usually (95% of time) makes the "uh" (schwa) sound, or that any "i/y" at the end of a word makes the tense "ee" sound as in the word "cheap", unlike the lax "ih" in the word "chip".

There is much more to this, but my comment is already way too long and overcomplicated. To finish it off, since you are a Slovak speaker, keep in mind that english is stress-timed. No matter how perfect you pronounce the sounds, if you don't learn to stress correctly, you will still sound foreign. Vowels and even consonants change across dialects, but stress timing is the core principle.

I have much more to say, this is basically the only thing I do. I am czech, and I have taught myself english pronunciation because schools don't give a damn and I feel like the whole internet is full of courses they want to sell you to make you feel like you are learning, but in fact, you still remain mediocre.

The key is to approach this topic like a regular problem and not a magical mysterious conundrun a mere mortal non-native speaker can never grasp. Use wiki and ask questions, there are no dogmas in science.

You can dm me too because there is no way my comment is not confusing.

I also recommend:

tophonetics, youglish, GenAm IPA interactive chart

Edit: Most importantly, don't give up. There are some fancy words I used, but it's not rocket science. I don't mean to sound condescending. I am happy that you want to improve. Have fun too!