I would defiantly do an alignment.
https://wranglertjforum.com/threads/how-to-align-your-jeep-wrangler-tj.85/
The driveshaft is not stock. looks like you have an SYE
When I did my swap I had to shorten the drivehaft a bit in order to make it fit. The dana 44 housing is a bit longer then the 35. You can get away with pushing the axle backwards if you have adjustable arms but it is a band-aid not a fix. I did that temporarily with my jeep and the shock was contacting the exhaust.
A driveshaft shop can do it for you or you can give tom woods a call and ship them yours.
You will also need a conversion joint or a new yoke to connect the current driveshaft to the 44. Here is the link to the one I used.
https://www.amazon.com/gp/product/B000CKP1PW/?tag=wranglerorg-20
@Jerry has good input on this. If I remember correctly he prefers a new yoke which would have you use your old ujoint. He will correct me if I'm wrong I'm sure.
You may be able to swap the yoke from the dana 35 to the 44 but I'm not certain on that.
I did since it was completely apart anyways. I also replaced the inner seals while it was out since I didn't have any history on the axles.