Hi there and welcome
I think you might have a prop issue (swing) as well as in an undertired/overtired loop as it looks like she might need more A and is undertired, which is why she'd be fighting you. At this age, we stopped going by the cues and started going by the clock (within reason, of course). Most 4.5mo's would be on 4hr EASY and that means 2hrs A time.
Average A times- BOOKMARK ME! So I would aim for something like this:
7am - wake and eat
9-10.30 - morning nap (doesn't have to be 2hrs long)
Eat when wakes
12.30-2/2.30 - afternoon nap (doesn't have to be 2hrs long)
Eat when wakes
4.30 - catnap (usually 30-45mins)
E - cluster feed
7pm - final E and bedtime
I would try and do the morning and afternoon nap in the cot and you could do the last nap/catnap in the swing if desired. Usually the last nap starts to disappear by 6/7 months (sometimes earlier) and some parents APOP this nap.
If she knows how to self soothe with her thumb, you could gently try and guide her hand to her mouth... but you may find that if she's tired enough to sleep (with the increased A), she will do that on her own. Otherwise, I would suggest the shh/pat method. If she's not crying though there is no need to shh/pat her. If she is, stay with her and shh/pat her until she's settled. Make sure you have a good windown routine so that she knows S is coming up. It doesn't have to be anything fancy - we change nappy, close blinds, put on white noise and I sway with her for a few minutes and then pop her in her cot.
Here is a link on how to transition:
3-4hr EASY Transition – In 5 Minute IncrementsAt night, I used to try and stick to the same feeding schedule as during the day - so if she wakes anywhere from 4hrs onwards, feed her and pop her back to sleep but if its before, try and settle her with shh/pat. Just make sure she isn't genuinely hungry though because there is a big GS at 4 months.
See how you go and let me know if you have any questions