Is there such a thing as "bottling up too much"?

For as long as I can remember since I was a child, I would remember crying and my mom would hit me shouting "boys dont cry!" at me, then thats when I started trying to bottle things up. Recently, when ever Im mad or sad I just bottle it up, forget it, then move on with my life not letting it bother me because there is no reason for me to be be in a negative mood when I should be in a positive one. When I really do get sad I just shed some tears, take a deep breath, then move on.
Today (more like yesterday sense it's 12:54 am here) my friend went over to my school to pick up her friend, I walk over to her to say hi because we rarely see each other in person then she kinda took some of her anger on me(wont say why shes mad). I said "Im sorry", then she said "it isn't your fault, Im not mad at you".
I've never liked it when my friends or the people I care about are in a bad mood (who wouldn't), it makes me sad really, especially when it's a situation where I can't help them. I know it's out of my control and sh*t happens but I would at least like to help a friend out. When Im around a friend who is mad I just bite my lip and keep myself shut because I don't know what to say or do to cheer them up so I give them space if things dont cool down. I know some people might think it's stupid feeling sad just because a friend is having an off day but I honestly don't know where it came from. I don't mind if people think it's stupid because I'm pretty much the person who keeps things to himself (a lot).
Here is where things might not make any sense because I don't know how to explain it that well and the main reason why Im asking if there is such a thing as "bottling up too much". I thought of my friend and for some reason a tear started to surface, then countless more after that with being reminded of all the things I've bottled up in the past. I felt like I was drowning in my own tears. I guess Im frugal? I don't know what to call it. Is it so wrong for caring for other people?

 

Bottling things up for a long time can be both mentally and emotional harmful, what you need is someone you trust enough to talk to, and the whole 'boy don't care' is bullcrap, we can all cry if we really need to. And it's not wrong to care for other people.