I fed my DD formula occasionally when she was a week old and then once a day from when she was around 19 weeks (tongue tie issues and I couldn't pump enough to feed her) - we found out later that she had a cow's milk protein intolerance when we found blood in her nappy and she had diarrhoea. It also contributed to her low weight gain (as well as the tongue tie)
In all honesty, it was early introduction of the formula which probably caused her intolerance through sensitisation. If I'd have waited until she was 6 months it would have been unlikely she'd have it (related to closed gut thing).
Intolerance / allergy isn't always immediate - can take time of exposure to the protein for it to develop (DM's a microbiologist, DH worked in toxicology and a close friend is a consultant pathologist working in immunology who explained how it can develop). Of course, it doesn't happen to every child (I was ff from 8 days and have no intolerances), which is why it didn't occur to me or DH when we gave DD the formula (plus we were pretty clueless about breastfeeding!).
However, I should have probably been more cautious as DSis is atopic (eczema, hayfever) and when she has lots of dairy it makes her eczema flare up - so there is a mild family history.
whereisthewitch there are varying degrees of intolerance - DD had no problems once she was ebf again and I'd re-introduced dairy into my diet.
As a pp said, I'd just be around the first few times you give formula and ask whoever's caring for him to just look out for him arching his back, green poo / diarrhoea. If you've no family history of allergies, I'd be surprised if he did react to it.
Sorry for the essay and hope I haven't scared you - as I said, I was ff and have no problems at all! Hope it works out for you and you get some time to yourself 