You cannot spoil a 10 week old with attention or love or cuddles, really you can't.
Please don't let leave such a tiny baby to cry, all you will teach him is that even when he tries his very hardest to get you, after all crying is all he can do, you still won't come.
Babies cry, endlessly, and often it will drive you crazy, a sling might be helpful so you can get on with stuff and he can still be close to you.
Don't feel bad for it getting to you, I often used to carry mine around when they were tiny, singing very softly and gently 'Go to sleep you bastard, go to sleep you shit, or mummys going to throw you, out the fucking window'
or some such, used to make me feel better.
Responding promptly to every cry at this age is the right thing to do (unless you are having a poo, then they might have to wait a sec
, I'm sure you are doing a great job, remember 'This too will pass'.