Alternatively, you could neuter him and get him a female companion to avoid male domination issues (a long an complicated story that you can read about in a lot of posts here). There are great and stable male/male pairs but it's not always possible/easy.
The squeeking you're hearing is called "wheeking". It's most often a cry for something (attention, food, affection).
Also, two weeks is very early for you to be picking him up and putting him on your lap while you work. Guinea pigs must be given time to settle at their own pace. Things must be taken slowly and patiently with them.
There are stages to go through before you can pick them up. Feeding them by hand, followed by feeding them by hand and gently petting them, followed by just gently petting them, followed by trying to pick them up and giving them a treat. If you're picking him up, you should give him a treat when you do so this is positive association (try a piece of cucumber, romain lettuce or grass).
Finally, as above, your guinea pig will never be happy on his own. No matter how strong a bond between owner and piggy (and there are some very affectionate and close bonds formed) this can never be enough for a guinea pig. They are social and (most importantly) vocally communicative animals. They have at least 12 distinguishable calls which only another guinea pig can answer.
The very best thing you can do for your guinea pig is to get him a friend, be it another male (boar) or a female (sow) - after neutering of course. There are also things like cage size, feeders, water etc. that you will need to think about if you get another piggy but there's loads of help and advice here for that too.
We are all here to try to help you with any concerns or questions and a lot of members know pretty much everything there is to know and are really nice. Don't be shy in asking any question no matter what it is
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