Can i be a master with low internet rating?

Hi. I have played chess in tournaments in real life and also took some chess lessons from a real life club.  And also from internet chess prigrams. I played many games online too and solve puzzles and know theory, but still my online rating is 1200 - 1400, depending on the time controls. I am very concerned that 1400- rated players are so tough for me and play very good, like masters and beat me most of the time. My questuon is can i still become a master with online rating of 1200 - 1400, knowing that online chess elo is not official? Or i am pretty much done and hopeless to become better? Let me know what your opinion is.

Without actually getting better, that rating isn't enough to get to close to being a master OTB.

So maybe i have reached the maximum level that i can reach in chess, no matter how much i play and train? For example there are players with thousands of games and still with rating only about 1000

The players who have thousands of games and there rating stays the same aren't trying to improve. The make the same mistakes over and over and dont learn. If you want to improve you have to recognise what you are doing wrong and make sure it doesn't happen again.

there is no max if you dedicate yourself and practice

Chess can be hard to solve even when one is ahead by – say a minor piece. If one underestimates one's opponent due to some arbitrary number, it becomes harder still. 

There is a realistic maximum that each player is likely to reach based on their ability and effort level. It takes work to move beyond that and the amount of work needed to reach any particular level will be dependent on the person attempting it.

At some point the amount of work needed to improve is going to come into conflict with other life factors. Whether any particular person can move beyond that depends on a number of factors.

Some people just study and play casually and may not see much, or any improvement. Some people primarily play because they enjoy the game and improving isn't something that is a motivation for them.

maybe i should play only for fun then. because its not possible for a normal person to get that good  i can't dedicate my life to chess.

Actualy, you may be a stronger player playing classic chess games.  But you also may be a weaker one, it depends on how used you are to computer and the table chess. Still, the difference may not be as much as from you go from newbie to master, but the internet or even your hardware may indeed be against you. Me, for exemple, I find I do way better playing on my mobile using the app than on my computer at home. My computer lags a lot, so at home I fear playing bullet and blitz. I've managed to jump my bullet rating from 400 to 600 almost instantly just by using the mobile instead of the computer and enabling the "premove". Then with some pratice I've been pushing my online boundaries.

im happy for you, man. at least you can improve 

If we are talking about FM masters, then your chess.com rating strength in blitz should be at least 2500.

Don't worry about masters, set realistic goal like achieving 2nd grade 1600-1800

even 1600 is too much for me. I once saw NM player with 1600 rating playing online here.