Estimating tasks is a requirement of software development. Get used to it. We never have perfect information for estimating.
What you do is break it up into tasks and estimate each one individually. Then you add an uncertainty factor of 30-200%, depending on how uncertain of your figure you are, per task. That is the time per task you give. Do not specify the uncertainty factor as a separate item in the spreadsheet you build. Just add it to the figure of what you think it will take. Then add it all up.
Then the next trick is to not assume an 8 hours day when determining the deadline from the total hours. If the total hours are 142 to accomplish the tasks, then divide by 6 not 8 to get the total number of days and determine the deadline. This accounts for unavoidable delay, time off, being asked to work on more urgent issues, required HR meetings and other admin tasks like timekeeping, etc. For a short project this may not be as important or you could get away with dividing by 7 but you need to start accounting for this in doing your estimating unless you want to spend the rest of your life working to unreasonable deadlines and working overtime to do so.
In determining tasks, make sure you include time for meetings, email reporting and other management communication that is required during the project. Also include other related tasks, like unit testing, creating a source control repository, responding to QA issues, deploying to other servers, etc. One of the biggest problems I have seen in estimating is that devs often only estimate the actual programming time, but all the other tasks added up often take as long or longer.
If your boss pushes back on your estimate, show him the details and ask what he thinks is too high and why. Ask him if there are steps you can skip. Ask him to prioritize the steps so that you get the most out of the actual time you have. Ask him if the scope can be reduced for this deadline. Find out what is the most important thing to get done.
You may find that if he needs it by a certain date, that he might expect you to work overtime. This is not unusual in this industry either especially when it is getting close to the deadline. It is not in your best interests to complain about that at this point as you may already be perceived as not contributing (this is my guess based on what you wrote about how little you seem to have done so far).
Next, it sounds as if you are feeling pressured to meet a deadline. Welcome to the real world, we all work on deadlines and have the pressure to meet it. You can't get away with making no progress from now on. You need to have something to show daily that you accomplished. This is not school where you can throw together the final project in the last weekend before exams. Every day, for the rest of your career you will need to be able to show what you did that day. This is a high pressure career, you need to learn to cope with that.
You also need to stop making excuses. Everyone knows you are new, but you need to be seen as digging in and working on accomplishing the task. If people perceive you as not working or being unable to do the work then that will have a negative impact on your pay, the type of work assignments you get and ultimately your employability. You need to manage your boss's perceptions of you at all times in the work world.
You also need to get rid of the attitude that you can't do this, right now. If you can't, then you don't belong in the profession. Maybe that sounds harsh, but the real world is harsh, you need to step up and perform. You can accomplish a huge amount in two weeks if you actually focus on work. Even if you miss the deadline, you need to be able to show that you accomplished something in that time beyond some nebulous research. If research is all you did because it is truly a complex problem, then be prepared to show documentation of that research. If I had someone do nothing but research for two weeks, I would expect to see several hundred pages of research notes.