I sometimes get religious doubts such as how do I know that the higher power is Allah? How do I know that the Quran is really the book of Allah? I wish these doubts would go away but I don't know what to do. How should I deal with them?
Real Islam of the Prophet (SAWA) and Ahlul Bayt (AS) provides authentic answer to any question and full explanation to every doubt.
You should never feel disturbed from any question or any doubt, but face it frankly and seek the answer from authentic scholars.
You mentioned a question: How to know that the higher power is Allah?
Answer: Allah is Creator of every creature in the universe and the sophisticated system in the creation and creatures proves that The Creator is One. Had another Gid existed, he should have declared his existence to the creature. Imam Ali (As) said : Had your Lord had a partner, the claimed partner should have sent messengers to people. All the messengers from Allah are the most noble and most truthful persons and all of them brought the message of Tawheed as the biggest fact in the existence.
You also mentioned a question: How to know that Quran is really from Allah?
Answer: The miracles in Quran prove with no doubt that Quran can never be from human source. Quran challenged the enemies who claimed that it is not from Allah, to brig any book like Quran using the help of every human and Jinn ( Say: If all human beings and all the Jinn join all their efforts to bring like this Quran,they will never bring like it, even if all of them joined their efforts)(Sura 17, Verse 88). When they failed, Quran challenged them to bring ten chapters similar to Quranic chapters which are 114 chapters. (They claim that Quran was created by you, Say: Bring you ten created chapters like Quran and call who so ever you can to help you other than Allah if you are truthful) (Sura Hood, verse 13). When they failed to do that again, Quran challenged them to bring just one chapter like Quranic chapters (If you are doubt about what We revealed on Our servant, then bring one chapter like it and call all you supporters besides Allah if you are truthful.) They again failed. This itself is an evidence that Quran is above the abilities of humans and Jinns and it is from Allah.
Scientific miracles in Quran also prove that it is from Allah. You can search in the internet (scientific miracles in Quran).
These questions can be from Satan to disturb you but you should worry but get the answer from authentic scholars.
Wassalam.