Wow! That is one I have felt trepidation over for some time myself. While I'm still pre-HRT and still a long way from going FT, I have had a few occasions where I had walked into the ladies restrooms. Of course the first several times don't actually qualify, because this was while I had been a restaurant manager and I would wait until the restaurant was closed and everyone (staff included) had left the building and I would (hesitantly) creep into the ladies room to take care of nature's call. Even when I knew I was the only one and that there was no way that I could be seen/caught I still had a strong apprehension. That may also been attributed to the fact that I was still in denial about being trans and going in there would open a lot of issues.
The only legitimate adventures were this past September when I attended the SCC (Southern Comfort Conference) and it was regarded as a kind of safe-zone for us to all use the restroom that we preferred or at least appropriate for how we were presenting (ladies room for me). Even though, by far, most of the women in there (the 3-4 times I went in that day) were trans, there were also a number of cis-women who were there as well. It felt wonderful to be able to just walk right in a act like I belong.
Fortunately for you, going into a men's room may prove easier. Just walk in and step into a stall, shut the door, take a deep (quiet) breath and do your thing. There is a kind of code with men in restrooms that you avoid eye contact and conversation - though there are exceptions, but those are usually people you know or know you. The best thing is to just go in with the mindset that that is where you belong - and you do. Judging by your avatar, you look like a late teen young man who is clean shaven. I wouldn't worry about it. The first few times are the worse, but if you psych yourself up and walk in with the confidence that you are a guy and this is the guys restroom, don't gawk, and take care of business, wash and exit, you'll do just fine.
I'm sure there are some restrooms that you could walk into wearing a ball gown and heels and not even be noticed.

Oh, another trick I just remembered (I've done this for so long I nearly forgot I do it). If you're in a place where you can keep a sideways glance at, or towards the restrooms, keep kind of a tally on the number of guys entering and leaving and the frequency and figure out how much time you can rely on where there you will be the only one in there. (I have always been uncomfortable and self-concious in the men's room - being a girl in the wrong shell)
Deanna