I'd think the refraining from weights is only temporary, while she's releasing the tight muscles that are causing the TOS (usually scalenes and pectoral muscles) and bony areas (1st rib). Normal physio progression would get you back to doing strengthening activities that balance what is going on with you. It is possible you may have been doing certain strength exercises that contributed to your TOS even though it seems like they haven't caused any noticeable effects for you while you're doing them.

And, swimming, yes, it can cause TOS troubles in some people. So making sure to let your physio know it doesn't work for you, so she can recommend a better choice for you.