Woah what a situation.
My instinct is to say can't you defer college a year but I guess you've thought of that. Having a baby under, I'd say, 3 months old and doing anythign else that requires full concentration and commitment is an extremely difficult ask of anyone, let alone with a week old baby.
I can only give my opinion so not saying I'm right with anything, but I'd be worried about bonding being away from baby for so long at such a young young age. I think you'd miss him terribly and the stress of missing him would far outweigh the 'rest' that you'd have to be honest, because baby is so young. You wouldn't be concentrating on college anyway. As you've asked if he's okay on bottles the week, does this mean you're bfing? If so that's a whole other issue to contend with.
I can understand why you're upset and we all need someone else to help us in early days. Is there no-one else who'd help? (no one at all from dad's side - mil, sil etc? - as I think anyone who could help out for a bit is better than baby being away full time). Is there a creche at college (not sure if they take such young babies though).
If I were you I'd defer college, for a year ideally but even for a term would be good (but that's me, that might not be right for you) but I'd certainly go in and see college on Monday and explain your circumstances, rather than let your mom take him for a whole week. Especially if there is no one else who can help, just your mom, you need to ensure the college is fully aware of that and they should make allowances. You look quite young on your profile pic (lucky you) and I don't think they'd say to someone my age (30s) any kind of 'warning' about attendance. They have to take extenuating circumstances into consideration no matter what they are regardless of age. If they shove you off the course for missing the first week when there really is NO other option then you could take it further as they're most certainly not allowed to do that. Why are you in such a rush to go to college? If you really want to, then you WILL go, no matter when.
Really hope you find a solution hun, but really, I'd stay with baby the week x