With my first child (DS) the sleep problem was really bad for the first 4 months. After that it improved gradually, in a non-linear way, by which I mean sometimes I'd wake up having had an unbroken 5 hours' sleep, feel like a new woman, think I'd cracked it, and then the next week might be bad again. But slowly the better nights got closer together and the bad nights fewer.
I did everything "wrong" with DS - tried sleep training but didn't stick at it, let him get in bed with me at 3am because I was so desperate for the crying to stop, etc. I don't know if it would have been better if I'd been more regimented. At 2 months babies aren't ready for sleep training though. As others have said, all you can do at this age is try to reduce daytime naps by waking baby up after, say, 90 minutes, keep them awake by undressing them a bit if necessary, that sort of thing. Eventually they will start sleeping longer at night to make up the sleep.
When my DS was 2.5 I had a DD, and she was also not a good sleeper, but with her I managed to get her into better habits a bit sooner. Several years later I had another DD, and by the time she was 4 months old she would go to bed at 7pm, wake 3-4 times in the night for a feed, and start the day anywhere between 5-7am. Then 3 naps in the day: 1 hour in the morning around 9-10, 2 hours at lunch around 12.30-2.30, and about 30 mins around 4.30pm.
A lot of the day/night sleep conundrum is about getting enough milk into them in the day so they aren't waking to feed all night. You need to wake baby up in the day to get them to feed more in daytime.
Everything in parenting is just a phase. The early baby phase is so so hard because you have no idea what you're doing and they can't tell you. I have spent years thinking "it'll be better when he starts solids", "it'll be better when he starts school", "it'll be better when he's got through the difficult teenage bit"... DS is 20 now and at uni. Everything does get better. New things come up. You worry again. It's normal. You're normal. No one has all the answers and everyone is really just muddling through as best they can.
Have you got a friend IRL you can talk to about how you're feeling?