How to give estimates when facing challenge?

Sorry to hear about how demotivating the process has been for you. Here are my thoughts:

• I highly recommend this other Q&A about missed estimates and deadlines.
• "In addition to that, I am not sure what I will say in order to justify if I can't meet the deadline." - In these situations, it's best to tell the truth and back it up with evidence. If there's some dependency, call it out and explain why you can't cover that portion on your end. When you give details like this, it's possible your manager or tech lead will explain a path where you can handle it on your own, which is a win. Something else I do for any larger task is to provide a breakdown of all the sub-tasks and a timeline to justify my estimate.
• "I notice a pattern with me which is that I usually need some help which I get either at the end of the day or the next day." - Can you proactively predict this and bake this into your estimate? Generally what frustrates teams and managers is when estimates are wrong and have to be changed on the fly. An aggressive estimate that needs to be corrected to something more reasonable is worse than an estimate that is more reasonable off the bat.

Adding on to this, it seems like your manager is fundamentally unsupportive. If they're not accommodating of the above points, no matter how clear and polite you are, I highly recommend looking to switch teams, find someone else as your main point of leadership/mentorship like a supportive tech lead, or exit the company. Here's our in-depth session about finding the best team/company for you.

A broader question to bring up is that the actual planning/estimation should be not be too expensive. Most of an engineers' time should be spent on execution, not the meta-work like giving updates or estimates.

Are other people on the team also feeling burdened by the stress + time it takes to provide an estimate? If so, that's something to (separately) bring up with your manager, on how to improve that process.