Can i sign in to my itunes account on a different computer?

I'm going to try and explain this as best as I can because I'm not very tech savy.

I purchased an ipod touch a few year ago, plugged it in to my laptop, downloaded itunes and added songs and shows and such. I could do it through the ipod directly or when it was plugged in through itunes on the computer.
I just purchased an iphone. Now here is my questions…
my boyfriend has a macbook pro. I no longer have the computer i added itunes too to use my ipod. When i plugged my iphone in to his computer itunes opened but it is in his name with his music.
can i access my itunes with my music? Will it still be there if i log in with my username and password? And how do i even do that?
or will i have to plug my ipod touch in, upload the music in to his itunes library, then back on to my phone?
Thanks if anyone can help and sorry if it didn't make a lot of sense.

From your iPod, backup all your songs to iCloud. Then sign in with your Apple account to your new computer and retrieve the songs you backed up from your iPod.
Done.

I had the same problem as you a little while ago. You can access your itunes account from another itunes account. You just have to log out of it and log in your old one.
I don't think you can upload all your songs from your ipod onto his library without swiping all the songs off the ipod.
Thats all I can help you with. I don't know much about the songs still being on the account thingy sorry.

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